Theory question 110
Trigonometry(a) Copy and complete the table for the relation y = 2cos x + 3sin x for 0° ≤ x ≤ 360°
x: 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, 330°, 360°
y: 2.00, 3.23, __, __, 1.6, __, __, −3.2, __, __, __, __, __
(b) Using a scale of 2cm to 30° on the x-axis and 2cm to one unit on the y-axis, draw the graph of y = 2cos x + 3sin x for 0° ≤ x ≤ 360°
(c) From your graph, find the (i) maximum value of y, correct to two decimal places; (ii) solution of the equation (2/3)cos x + sin x = 5/6
Show the model answer
(a) y = 2.00, 3.23, 3.60, 3.00, 1.60, −0.23, −2.00, −3.23, −3.60, −3.00, −1.60, 0.23, 2.00
(b) Smooth sine-shaped curve through these points
(c)(i) Maximum y ≈ 3.61 (exact value √13 ≈ 3.606, near x ≈ 56°)
(ii) Multiply by 3: 2cos x + 3sin x = 2.5; read where the curve meets y = 2.5: x ≈ 10° and x ≈ 102°
For (c)(ii) turn the equation into y = 2.5 by multiplying by 3.