Trig graphs GCSE lesson: sin, cos and tan from 0° to 360°, and solving sin x = k

Trig graphs: practice

Sketch the graph and the line before using the calculator. Give angles in degrees, to 1 decimal place unless they are exact. The stretch is optional.

Diagnostic question: choose and explain

1. sin⁻¹ 0.6 = 36.9°. Solve sin x = 0.6 for 0° ≤ x ≤ 360°.
   1. 36.9° and 143.1°
   2. 36.9° only
   3. 36.9° and 216.9°
   4. 36.9° and 323.1°

Practice questions

1. sin 90° = ___, cos 90° = ___ and cos 180° = ___
2. Which graph goes through the point (0°, 1)?
   1. y = cos x
   2. y = sin x
   3. y = tan x
3. y = tan x has no value at two angles between 0° and 360°: the smaller is ___ degrees and the larger is ___ degrees
4. cos 30° = √3/2. Solve cos x = √3/2 for 0° ≤ x ≤ 360°: the smaller x = ___ and the larger x = ___
5. How many solutions does sin x = 1.5 have between 0° and 360°?
   1. None
   2. One
   3. Two
6. sin 40° = 0.643 (to 3 decimal places). Which other angle between 0° and 360° has the same sine?
   1. 140°
   2. 220°
   3. 320°
   4. 50°
7. sin 60° = √3/2. Solve sin x = −√3/2 for 0° ≤ x ≤ 360°: the smaller x = ___ and the larger x = ___
8. What is the greatest value of y = sin x + 2?
   1. 3
   2. 1
   3. 2
9. Stretch: solve tan x = 1 for 0° ≤ x ≤ 360°: the smaller x = ___ and the larger x = ___

Support: For question 4: sketch y = cos x and the line y = √3/2, about 0.87. How many times do they meet? The cosine wave is mirrored in x = 180°: where is the second meeting?

Trig graphs: exit

A sketch with both answers marked.

1. Solve cos x = −0.5 for 0° ≤ x ≤ 360°. Sketch y = cos x and the line y = −0.5, and mark both answers on your sketch.

Exit check

One equation with a negative k shows who finds both answers from the graph.

Solve cos x = −0.5 for 0° ≤ x ≤ 360°.

Trig graphs: sketches and two answers

Sketch the graph and the line y = k before using the calculator. Give angles to 1 decimal place unless they are exact.