Theory question 109
Trigonometry(a) Copy and complete the table of values for y = 2 cos x + 3 sin x for 0° ≤ x ≤ 360°.
x: 0°, 60°, 120°, 180°, 240°, 300°, 360°
y: 2.0, __, __, __, −3.6, __, __
(b) Using a scale of 2 cm to 60° on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of y = 2 cos x + 3 sin x for 0° ≤ x ≤ 360°.
(c) Using the graph: (i) solve 2 cos x + 3 sin x = −1; (ii) find, correct to one decimal place, the value of y when x = 342°.
Show the model answer
Model answer
(a) y = 2.0, 3.6, 1.6, −2.0, −3.6, −1.6, 2.0
(b) Plot the points with the given scales and join with a smooth curve
(c)(i) Read where the curve meets y = −1: x ≈ 162° and x ≈ 310°
(ii) At x = 342°, y ≈ 1.0
Explanation
At 180°, cos x = −1 and sin x = 0, so y = −2.0.