Theory question 110
Trigonometry(a) Using a scale of 2 cm to 30° on the x-axis and 2 cm to 0.2 units on the y-axis, on the same graph sheet, draw the graphs of y = sin 2x and y = cos x for 0° ≤ x ≤ 210° at intervals of 30°.
(b) Using the graphs in 10(a), find the truth set of: (i) sin 2x = 0; (ii) sin 2x − cos x = 0.
Show the model answer
Model answer
(a) x: 0, 30, 60, 90, 120, 150, 180, 210
sin 2x: 0, 0.87, 0.87, 0, −0.87, −0.87, 0, 0.87
cos x: 1, 0.87, 0.5, 0, −0.5, −0.87, −1, −0.87
Plot both smooth curves on the same axes.
(b)(i) Where y = sin 2x crosses the x-axis: x = 0°, 90°, 180°.
(ii) Where the curves meet: x = 30°, 90°, 150°.
Explanation
The truth set in (ii) is where the two curves intersect.