(a) Copy and complete the following table of values for (y = 3sin 2theta – cos theta).
| (theta) | 0° | 30° | 60° | 90° | 120° | 150° | 180° |
| y | -1.0 | 0 | 1.0 |
(b) Using a scale of 2cm to 30° on the (theta) axis and 2cm to 1 unit on the y- axis, draw the graph of (y = 3 sin 2theta – cos theta) for (0° leq theta leq 180°).
(c) Use your graph to find the : (i) solution of the equation (3 sin 2theta – cos theta = 0), correct to the nearest degree; (ii) maximum value of y, correct to one decimal place.
Explanation
(a)
| (theta) | 0° | 30° | 60° | 90° | 120° | 150° | 180° |
| y | -1.0 | 1.732 | 2.098 | 0 | -2.098 | -1.732 | 1.0 |
(b)
(c)(i) Solution of (3 sin 2 theta – cos theta = 0) is at y = 0
= (9.30°, 80°, 174°)
(ii) Maximum value of y = 2.098 (approxeq) 2.1 (to 1 decimal place)