Theory question 112
Trigonometryx: 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, 330°, 360°
y: 2.0, __, __, 3.0, 1.6, __, −2.0, __, −3.6, −3.0, __, __, 2.0
(a) Copy and complete the table of values, correct to one decimal place, for the relation y = 3sin x + 2cos x for 0° ≤ x ≤ 360°.
(b) Using scales of 2 cm to 30° on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of the relation y = 3sin x + 2cos x for 0° ≤ x ≤ 360°.
(c) Use the graph to solve: (i) 3sin x + 2cos x = 0; (ii) 2 + 2cos x + 3sin x = 0.
Show the model answer
(a) x = 30°: 3.2; 60°: 3.6; 150°: −0.2; 210°: −3.2; 300°: −1.6; 330°: 0.2
(b) Plot the points and join them with a smooth wave (maximum about 3.6 near 56°, minimum about −3.6 near 236°).
(c)(i) Where the curve cuts y = 0: x ≈ 146° and x ≈ 326°
(ii) 3sin x + 2cos x = −2: where the curve meets y = −2: x ≈ 180° and x ≈ 293°
For (c)(ii) rearrange to 3sin x + 2cos x = −2 and draw the line y = −2.