CLASS 11 MATHS · TRIGONOMETRIC FUNCTIONS

Trigonometric values of any angle and allied angles

Reduce the angle to an acute reference angle, then fix the sign by quadrant (All, Sin, Tan, Cos positive in quadrants I to IV). At 90° or 270° ± θ the function changes to its co-function.

Loading practice…

Worked examples

Example 1 · level 1

Find the value of tan 300°.

−1/√3
√3
1/√3
−√3

Show solution

300° → 300° (quadrant IV), reference angle 60°.
tan 60° = √3.
With the sign: tan 300° = −√3.

Answer: −√3

Example 2 · level 2

Find the value of tan 405°.

1/2
−1
−1/2
1

Show solution

405° → 45° (quadrant I), reference angle 45°.
tan 45° = 1.
With the sign: tan 405° = 1.

Answer: 1

Example 3 · level 3

Find the exact value of cos 75°.

(√3 − 1)/2
2 + √3
(√3 + 1)/2
(√6 − √2)/4

Show solution

cos 75° = cos(45° + 30°).
cos(A + B) = cos A cos B − sin A sin B.
Simplifying gives (√6 − √2)/4.

Answer: (√6 − √2)/4