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.

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 $= 1 / 2 + 1 / 2 = 1$ .

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 $\cos (37)$ .
$\cos 37 ° \approx 0.799$ .

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

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

Common mistakes

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

Year 10: Evaluating trigonometric functions

Exact values you should know

Using a calculator

Choosing the right function

Common mistakes

Skills to practise