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This page introduces fundamental Step-by-step trigonometry solutions GCSE with two starter problems focusing on sine and tangent ratios.
Example: Question 1 demonstrates finding a hypotenuse using sine ratio with Sin 35° = 20/x, resulting in x = 34.9
Vocabulary: Opposite - The side opposite to the angle in question Adjacent - The side adjacent to the angle in question Hypotenuse - The longest side of a right-angled triangle
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This section progresses to more complex calculations involving inverse trigonometric functions.
Example: Question 3 uses inverse cosine (cos⁻¹) to find an angle where cos θ = 16/24
Highlight: Both questions on this page require understanding of inverse trigonometric functions to find angles rather than sides.
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This page focuses on calculating unknown side lengths using trigonometric ratios.
Definition: Tangent ratio is used when working with opposite and adjacent sides (TOA in SOHCAHTOA)
Example: Question 5 uses tan 35° to find a length of 14.0 units
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These questions focus on determining unknown angles using inverse trigonometric functions.
Highlight: Question 7 demonstrates the use of inverse sine (sin⁻¹) to find an angle of 18.2°
Example: Question 8 uses inverse tangent to calculate an angle of 60.9°
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This page introduces more sophisticated problems involving multiple steps.
Example: Question 9 requires finding an angle in a complex shape involving multiple right triangles
Highlight: The solution requires breaking down the problem into manageable steps using basic trigonometric ratios
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This section presents more challenging problems requiring multiple steps and precise calculations.
Example: Question 10 involves using the Pythagorean theorem alongside trigonometric ratios
Highlight: Solutions must be given to 1 decimal place, emphasizing the importance of accuracy
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The worksheet concludes with the most challenging question requiring multiple steps and careful analysis.
Example: Question 11 involves finding an angle in a complex triangle setup using multiple trigonometric calculations
Highlight: The final answer must be given to 1 decimal place (41.8°)
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This page outlines the essential guidelines for approaching these SOHCAHTOA exam problems worksheet. The document is designed for GCSE mathematics students.
Highlight: Students must use black ink or ball-point pen and show all working out.
Definition: SOHCAHTOA is a mnemonic device used to remember the relationships between angles and sides in right-angled triangles.
The page emphasizes proper exam technique including time management and thorough checking of answers.
