Theory question 110
Trigonometry(a) Copy and complete the following table of values for y = 3 sin 2θ − cos θ
θ: 0°, 30°, 60°, 90°, 120°, 150°, 180°
y: −1.0, , , 0, , , 1.0
(b) Using a scale of 2cm to 30° on the θ axis and 2cm to 1 unit on the y axis, draw the graph of y = 3sin 2θ − cos θ for 0° ≤ θ ≤ 180°.
(c) Use your graph to find the: (i) solution of the equation 3 sin 2θ − cos θ = 0, correct to the nearest degree; (ii) maximum value y, correct to one decimal place.
Show the model answer
(a) θ = 0° → −1.0; 30° → 1.7; 60° → 2.1; 90° → 0; 120° → −2.1; 150° → −1.7; 180° → 1.0
(b) Plot the points with the given scales and join with a smooth curve.
(c)(i) Read where the curve cuts the θ-axis: θ ≈ 10°, 90° and 170° (exact: cos θ(6 sin θ − 1) = 0 gives 9.6°, 90°, 170.4°)
(ii) Maximum y ≈ 2.3 (at about θ = 49°)
y is zero where the curve crosses the θ-axis.