Year 10: Evaluating trigonometric functions

Evaluating trigonometric functions means finding values of $\sin$ , $\cos$ , or $\tan$ for a given angle. In Year 10, this often begins with familiar exact angles and then moves into calculator work.

Use degree mode unless the question clearly says radians.

Work through the sections in order, then try the linked Year 10 skill quizzes after each section.

Exact values you should know

Some basic values appear again and again. For example, $\sin 30 ° = 1 / 2$ , $\cos 60 ° = 1 / 2$ , and $\tan 45 ° = 1$ .

Example 1: Evaluate

\sin 30 ° + \cos 60 °

$\sin 30 ° = 1 / 2$ .
$\cos 60 ° = 1 / 2$ .
Total $= 1 / 2 + 1 / 2 = 1$ .

Skill quiz: Evaluate familiar angles

Practise exact sine, cosine and tangent values before using decimal approximations.

Evaluate trigonometric functions

Using a calculator

For angles such as $37 °$ or $68 °$ , use the calculator. Check that it is in degree mode before pressing the trig key.

Example 2: Evaluate

\cos 37 °

Make sure the calculator is in degrees.
Enter $\cos (37)$ .
$\cos 37 ° \approx 0.799$ .

Skill quiz: Evaluate in the correct angle mode

Check the angle units and calculator mode, then round only the final answer.

Evaluate trigonometric functions

Choosing the right function

In triangle problems, the function depends on the sides involved. A common memory aid is $SOH - CAH - TOA$ .

Example 3: In a right-angled triangle, the opposite side is

4

and the hypotenuse is

5

. Find

\sin θ

$\sin θ = opposite / hypotenuse$ .
$\sin θ = 4 / 5 = 0.8$ .

Skill quiz: Match the ratio to the sides

Label opposite, adjacent and hypotenuse before choosing sine, cosine or tangent.

Trigonometric functions and trianglesPremium

Common mistakes

Leaving the calculator in radian mode.
Mixing up opposite, adjacent, and hypotenuse.
Rounding too early in a multi-step question.

Skill quizzes: Check angle mode and side names

Review numerical evaluations, then check the chosen ratio in triangle questions.