Theory question 106
Trigonometry(a) Copy and complete the table of values for the relation y = 3 sin 2x.
x: 0°, 15°, 30°, 45°, 60°, 75°, 90°, 105°, 120°, 135°, 150°
y: 0.0, __, __, __, __, 1.5, __, __, __, __, −2.6
(b) Using a scale of 2 cm to 15° on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of y = 3 sin 2x for 0° ≤ x ≤ 150°.
(c) Use the graph to find the truth set of: (i) 3 sin 2x + 2 = 0; (ii) (3/2) sin 2x = 0.25.
Show the model answer
Model answer
(a) y = 0.0, 1.5, 2.6, 3.0, 2.6, 1.5, 0.0, −1.5, −2.6, −3.0, −2.6
(b) Plot the points and join with a smooth curve
(c)(i) 3 sin 2x = −2: read where the curve meets y = −2, x ≈ 111°
(ii) Doubling gives 3 sin 2x = 0.5: read where the curve meets y = 0.5, x ≈ 5° and x ≈ 85°
Explanation
Rearrange each equation into the form 3 sin 2x = k, then draw the line y = k.