GCSE Maths · Maths
Trigonometry: a clear study guide
Trigonometry links an angle to the sides of a right-angled triangle. Label the known and unknown sides first, choose the ratio containing them and keep the calculator in the correct angle mode.
Choose the ratio
Relative to the chosen angle, the hypotenuse is opposite the right angle, the opposite side is across from the angle and the adjacent side touches the angle without being the hypotenuse. SOHCAHTOA links sine, cosine and tangent to these sides.
Use sine for opposite and hypotenuse, cosine for adjacent and hypotenuse, and tangent for opposite and adjacent. Write the ratio before substituting values.
- Sine = opposite / hypotenuse.
- Cosine = adjacent / hypotenuse.
- Tangent = opposite / adjacent.
Find a side or an angle
For a missing side, substitute the angle and known side then rearrange. For a missing angle, use the inverse button on the calculator, such as sin^-1, cos^-1 or tan^-1. Round only at the end unless the question says otherwise.
Draw or mark the right angle and check that the side you call the hypotenuse is the longest side.
Apply the result to a problem
In bearings, measure clockwise from north and write three figures, such as 035 degrees. In a word problem, state what the calculated length or angle represents and include units where appropriate.
Quick check
Which side is always the hypotenuse?
Answer: The side opposite the right angle.
What should you check before using a trigonometric ratio?
Answer: Identify the chosen angle and label the opposite, adjacent and hypotenuse sides relative to it.
Common questions
Why is my trigonometry answer different from the mark scheme?
Check the calculator is in degree mode, the correct ratio is used and rounding has not been applied too early.
Can I use trigonometry in a non-right-angled triangle?
SOHCAHTOA applies to right-angled triangles. Other triangle problems may require the sine rule, cosine rule or area formula if those methods are in your course.