Subjects

Careers

Open the App

Subjects

How to Solve Trigonometry Problems Step by Step for Beginners

Open

16

1

user profile picture

Courtney

03/01/2023

Maths

What is Trigonometry and how to solve it

Subjects

/

Maths

/

Geometry and measure

/

Angles, lines and polygons

/

Triangles

How to Solve Trigonometry Problems Step by Step for Beginners

Trigonometry is a branch of mathematics dealing with relationships between side lengths and angles of triangles. This guide covers the basics of solving trigonometric problems step by step for beginners, including labeling triangles, using SOH CAH TOA, and finding missing sides and angles.

Key points:

  • Learn to label triangle sides as opposite, adjacent, and hypotenuse
  • Understand and apply the SOH CAH TOA formula
  • Practice solving for missing sides and angles using trigonometric ratios
  • Use a calculator to compute trigonometric functions and inverse functions
...

03/01/2023

374

o Trigonometry Hypotenuse Angle och auch Steps: 1. Label the triangle 2. Pick correct Formula. 3. Set up the equation. 4 Souve it Adjacent H

View

Finding Missing Sides Using Trigonometry

This page demonstrates how to solve trigonometric equations with sin and cos to find missing sides in a right-angled triangle.

Example: To find the opposite side xx in a triangle with hypotenuse 12m and angle 35°:

  1. Identify the given information: angle = 35°, hypotenuse = 12m
  2. Choose the appropriate formula: Sin θ = Opposite / Hypotenuse
  3. Set up the equation: Sin 35° = x / 12
  4. Solve for x: x = 12 × Sin 35° = 6.88 roundedrounded

Highlight: When solving for a side, multiply if the known side is in the denominator of the ratio, and divide if it's in the numerator.

o Trigonometry Hypotenuse Angle och auch Steps: 1. Label the triangle 2. Pick correct Formula. 3. Set up the equation. 4 Souve it Adjacent H

View

Using Tangent to Find Missing Sides

This section explains how to solve trigonometric ratios using the tangent function to find missing sides in a right-angled triangle.

Example: To find the adjacent side xx in a triangle with opposite side 15m and angle 18°:

  1. Identify the given information: angle = 18°, opposite = 15m
  2. Choose the appropriate formula: Tan θ = Opposite / Adjacent
  3. Set up the equation: Tan 18° = 15 / x
  4. Solve for x: x = 15 / Tan 18° = 13.51 roundedrounded

Highlight: When solving for the adjacent side using tangent, divide the opposite side by the tangent of the angle.

o Trigonometry Hypotenuse Angle och auch Steps: 1. Label the triangle 2. Pick correct Formula. 3. Set up the equation. 4 Souve it Adjacent H

View

Finding Missing Angles in Trigonometry

This page covers how to solve trigonometric equations to find missing angles in a right-angled triangle.

Steps to find a missing angle:

  1. Label the sides of the triangle
  2. Identify the known sides
  3. Choose the appropriate trigonometric ratio
  4. Set up the equation and solve for the angle using inverse trigonometric functions

Example: To find angle x in a triangle with adjacent side 3cm and hypotenuse 8cm:

  1. Identify the given information: adjacent = 3cm, hypotenuse = 8cm
  2. Choose the appropriate formula: Cos x = Adjacent / Hypotenuse
  3. Set up the equation: Cos x = 3 / 8
  4. Solve for x using inverse cosine: x = Cos⁻¹3/83/8 = 67.98° roundedrounded

Highlight: Use a calculator to solve trigonometric equations involving inverse functions like Cos⁻¹, Sin⁻¹, or Tan⁻¹.

Similar content

Know Entire Nat 5 Maths Notes (Part 2): Applications thumbnail

7

455

S4/S5

Entire Nat 5 Maths Notes (Part 2): Applications

Part 2 of all the notes for National 5 Maths (adjusted for Covid so some topics may be missing)

Know Sin and Cos rules thumbnail

7

307

S3/S4

Sin and Cos rules

made for N5 maths. Please check my page for more N5 maths topics.

Know trigonometry and quadratics thumbnail

24

457

S4

trigonometry and quadratics

area of triangle, triangle trig, sine rule, angel sine rule, 2 part sine rule, bearings, cosine rule, angel cosine rule. QUADRATICS- quadratic functions, quadratic graphs,

Know Non-calculator Trig - National 5 Maths thumbnail

4

184

S4

Non-calculator Trig - National 5 Maths

jotter scan from the topic non-calculator trig from the national 5 maths course. Includes worked examples :)

Know HIGHER MATH NOTES thumbnail

432

6279

10/11

HIGHER MATH NOTES

NOTES

Know Year 7 Module 8 - Angles thumbnail

11

403

10/11

Year 7 Module 8 - Angles

NOTES

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

21 M

Pupils love Knowunity

#1

In education app charts in 17 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

Maths

Geometry and measure

Angles, lines and polygons

Triangles

 

Maths

•

374

•

3 Jan 2023

•

4 pages

How to Solve Trigonometry Problems Step by Step for Beginners

user profile picture

Courtney

@courtney01

Trigonometry is a branch of mathematics dealing with relationships between side lengths and angles of triangles. This guide covers the basics of solving trigonometric problems step by step for beginners, including labeling triangles, using SOH CAH TOA, and finding... Show more

o Trigonometry Hypotenuse Angle och auch Steps: 1. Label the triangle 2. Pick correct Formula. 3. Set up the equation. 4 Souve it Adjacent H

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Finding Missing Sides Using Trigonometry

This page demonstrates how to solve trigonometric equations with sin and cos to find missing sides in a right-angled triangle.

Example: To find the opposite side xx in a triangle with hypotenuse 12m and angle 35°:

  1. Identify the given information: angle = 35°, hypotenuse = 12m
  2. Choose the appropriate formula: Sin θ = Opposite / Hypotenuse
  3. Set up the equation: Sin 35° = x / 12
  4. Solve for x: x = 12 × Sin 35° = 6.88 roundedrounded

Highlight: When solving for a side, multiply if the known side is in the denominator of the ratio, and divide if it's in the numerator.

o Trigonometry Hypotenuse Angle och auch Steps: 1. Label the triangle 2. Pick correct Formula. 3. Set up the equation. 4 Souve it Adjacent H

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Using Tangent to Find Missing Sides

This section explains how to solve trigonometric ratios using the tangent function to find missing sides in a right-angled triangle.

Example: To find the adjacent side xx in a triangle with opposite side 15m and angle 18°:

  1. Identify the given information: angle = 18°, opposite = 15m
  2. Choose the appropriate formula: Tan θ = Opposite / Adjacent
  3. Set up the equation: Tan 18° = 15 / x
  4. Solve for x: x = 15 / Tan 18° = 13.51 roundedrounded

Highlight: When solving for the adjacent side using tangent, divide the opposite side by the tangent of the angle.

o Trigonometry Hypotenuse Angle och auch Steps: 1. Label the triangle 2. Pick correct Formula. 3. Set up the equation. 4 Souve it Adjacent H

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Finding Missing Angles in Trigonometry

This page covers how to solve trigonometric equations to find missing angles in a right-angled triangle.

Steps to find a missing angle:

  1. Label the sides of the triangle
  2. Identify the known sides
  3. Choose the appropriate trigonometric ratio
  4. Set up the equation and solve for the angle using inverse trigonometric functions

Example: To find angle x in a triangle with adjacent side 3cm and hypotenuse 8cm:

  1. Identify the given information: adjacent = 3cm, hypotenuse = 8cm
  2. Choose the appropriate formula: Cos x = Adjacent / Hypotenuse
  3. Set up the equation: Cos x = 3 / 8
  4. Solve for x using inverse cosine: x = Cos⁻¹3/83/8 = 67.98° roundedrounded

Highlight: Use a calculator to solve trigonometric equations involving inverse functions like Cos⁻¹, Sin⁻¹, or Tan⁻¹.

o Trigonometry Hypotenuse Angle och auch Steps: 1. Label the triangle 2. Pick correct Formula. 3. Set up the equation. 4 Souve it Adjacent H

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Introduction to Trigonometry

Trigonometry is the study of relationships between angles and sides in right-angled triangles. This page introduces the fundamental concepts and steps for solving trigonometry problems easily.

The three main steps to solve trigonometric problems are:

  1. Label the triangle
  2. Pick the correct formula
  3. Set up and solve the equation

Vocabulary:

  • Hypotenuse: The longest side of a right-angled triangle, opposite the right angle
  • Opposite: The side opposite to the angle in question
  • Adjacent: The side next to the angle in question

Definition: SOH CAH TOA is a mnemonic device used to remember the trigonometric ratios:

  • Sin θ = Opposite / Hypotenuse
  • Cos θ = Adjacent / Hypotenuse
  • Tan θ = Opposite / Adjacent

Highlight: Trigonometry is used to calculate missing sides or angles in right-angled triangles.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

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 it’s 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 didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m 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 😍😁😲🤑💗✨🎀😮

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 it’s 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 didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m 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 😍😁😲🤑💗✨🎀😮

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