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Maths
13 Dec 2025
438
2 pages
Trigonometry might seem intimidating, but it's actually just a clever way to find missing sides and angles in... Show more
Trigonometry is all about relationships in right-angled triangles, and there are three key formulas you need to remember. Think of them as your mathematical toolkit for solving triangle mysteries!
The three trigonometric ratios are Sin x = opposite/hypotenuse, Cos x = adjacent/hypotenuse, and Tan x = opposite/adjacent. The hypotenuse is always the longest side, the opposite is the side across from your angle, and the adjacent is the remaining side next to your angle.
Here's your game plan first, work out which two sides are involved in your question. Then pick the formula that uses those two sides - it's that simple!
When you need to find an angle, use the inverse function by pressing 'shift' or '2nd' followed by sin, cos, or tan on your calculator. Just make sure your calculator is in DEG mode, and you'll see sinโปยน, cosโปยน, or tanโปยน appear on screen.
Top Tip Remember SOH-CAH-TOA to recall which ratio uses which sides Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
Sometimes you'll encounter isosceles triangles where two sides are equal - don't panic! You can split them down the middle to create a right-angled triangle that you can actually work with.
In the example with a 25m isosceles triangle, splitting it creates a right triangle where the adjacent side becomes 15m and the hypotenuse stays 25m. Since you know adjacent and hypotenuse, you use cosine.
The calculation becomes cos x = 15/25 = 0.6, then use the inverse to find x = cosโปยน(0.6) = 53.1ยฐ. Remember to round to the required decimal places - in this case, 1 decimal place.
The key is identifying which sides you know and which trigonometric ratio connects them. Once you've got that sorted, it's just a matter of plugging numbers into your calculator!
Remember When finding angles, you'll always use the inverse functions (sinโปยน, cosโปยน, tanโปยน) on your calculator - this 'undoes' the original ratio to give you the angle.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help โ all at your fingertips.
7
Smart Tools NEW
Transform this note into: โ 50+ Practice Questions โ Interactive Flashcards โ Full Mock Exam โ Essay Outlines
Explore the detailed mark scheme for the OCR GCSE Higher Mathematics Paper 6 from June 2018. This resource covers key concepts such as triangle congruence, vector addition, area calculations, and more, providing essential guidance for exam preparation and understanding of marking criteria.
MathsExplore the methods for calculating the area of various quadrilaterals, including squares, rectangles, and parallelograms. This summary covers essential formulas, properties, and examples to enhance your understanding of area and perimeter in geometry.
MathsExplore the fundamentals of bearings in geometry, including angle measurement, relationships, and rules. This summary covers key concepts such as calculating bearings, angle pairs, and the total angles in triangles. Ideal for students preparing for exams or seeking to enhance their understanding of geometry.
MathsPrepare for your GCSE exams with this comprehensive non-calculator practice paper. Covering key concepts such as area of triangles, ratios, statistical averages, and more, this resource includes 22 questions with varying marks to help you master essential mathematical skills. Ideal for students aiming for higher grades, this practice paper is designed to enhance your problem-solving abilities and exam readiness.
MathsExplore essential circle theorems, including properties of inscribed quadrilaterals, central angles, and angle bisectors. This summary covers key concepts such as congruent chords, angles subtended by arcs, and the relationship between tangents and radii. Ideal for quick revision and understanding of circle geometry.
MathsExplore the fundamentals of bearings in geometry, including how to measure angles accurately and the importance of using three digits. This summary covers key concepts such as angle relationships and measurement techniques, essential for mastering this topic in your studies.
MathsQuotes from every main character
English LiteratureApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Trigonometry might seem intimidating, but it's actually just a clever way to find missing sides and angles in right-angled triangles. Once you master the three basic formulas (sin, cos, and tan), you'll be solving triangle problems like a pro!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Trigonometry is all about relationships in right-angled triangles, and there are three key formulas you need to remember. Think of them as your mathematical toolkit for solving triangle mysteries!
The three trigonometric ratios are: Sin x = opposite/hypotenuse, Cos x = adjacent/hypotenuse, and Tan x = opposite/adjacent. The hypotenuse is always the longest side, the opposite is the side across from your angle, and the adjacent is the remaining side next to your angle.
Here's your game plan: first, work out which two sides are involved in your question. Then pick the formula that uses those two sides - it's that simple!
When you need to find an angle, use the inverse function by pressing 'shift' or '2nd' followed by sin, cos, or tan on your calculator. Just make sure your calculator is in DEG mode, and you'll see sinโปยน, cosโปยน, or tanโปยน appear on screen.
Top Tip: Remember SOH-CAH-TOA to recall which ratio uses which sides: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Sometimes you'll encounter isosceles triangles where two sides are equal - don't panic! You can split them down the middle to create a right-angled triangle that you can actually work with.
In the example with a 25m isosceles triangle, splitting it creates a right triangle where the adjacent side becomes 15m and the hypotenuse stays 25m. Since you know adjacent and hypotenuse, you use cosine.
The calculation becomes: cos x = 15/25 = 0.6, then use the inverse to find x = cosโปยน(0.6) = 53.1ยฐ. Remember to round to the required decimal places - in this case, 1 decimal place.
The key is identifying which sides you know and which trigonometric ratio connects them. Once you've got that sorted, it's just a matter of plugging numbers into your calculator!
Remember: When finding angles, you'll always use the inverse functions (sinโปยน, cosโปยน, tanโปยน) on your calculator - this 'undoes' the original ratio to give you the angle.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help โ all at your fingertips.
7
Smart Tools NEW
Transform this note into: โ 50+ Practice Questions โ Interactive Flashcards โ Full Mock Exam โ Essay Outlines
Explore the detailed mark scheme for the OCR GCSE Higher Mathematics Paper 6 from June 2018. This resource covers key concepts such as triangle congruence, vector addition, area calculations, and more, providing essential guidance for exam preparation and understanding of marking criteria.
MathsExplore the methods for calculating the area of various quadrilaterals, including squares, rectangles, and parallelograms. This summary covers essential formulas, properties, and examples to enhance your understanding of area and perimeter in geometry.
MathsExplore the fundamentals of bearings in geometry, including angle measurement, relationships, and rules. This summary covers key concepts such as calculating bearings, angle pairs, and the total angles in triangles. Ideal for students preparing for exams or seeking to enhance their understanding of geometry.
MathsPrepare for your GCSE exams with this comprehensive non-calculator practice paper. Covering key concepts such as area of triangles, ratios, statistical averages, and more, this resource includes 22 questions with varying marks to help you master essential mathematical skills. Ideal for students aiming for higher grades, this practice paper is designed to enhance your problem-solving abilities and exam readiness.
MathsExplore essential circle theorems, including properties of inscribed quadrilaterals, central angles, and angle bisectors. This summary covers key concepts such as congruent chords, angles subtended by arcs, and the relationship between tangents and radii. Ideal for quick revision and understanding of circle geometry.
MathsExplore the fundamentals of bearings in geometry, including how to measure angles accurately and the importance of using three digits. This summary covers key concepts such as angle relationships and measurement techniques, essential for mastering this topic in your studies.
MathsQuotes from every main character
English LiteratureApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Sociology