Theory question 109
Trigonometry(a) Copy and complete the table of values for y = 3 sin x + 7 cos x for 0° ≤ x ≤ 180°.
x: 0°, 20°, 40°, 60°, 80°, 100°, 120°, 140°, 160°, 180°
y: 7.0, __, __, __, 4.2, __, −0.9, __, __, __
(b) Using a scale of 2cm to 20° on the x-axis and 2cm to 2 units on the y-axis, draw the graph of y = 3 sin x + 7 cos x for 0° ≤ x ≤ 180°.
(c) Using the graph, find the: (i) value of y when x = 150°; (ii) range of values of x for which y > 0.
Show the model answer
Model answer
(a) y = 7.0, 7.6, 7.3, 6.1, 4.2, 1.7, −0.9, −3.4, −5.6, −7.0
(b) Plot the points and join with a smooth curve
(c)(i) At x = 150°, y ≈ −4.6
(ii) The curve is above the x-axis from x = 0° to where it crosses at about 113°: 0° ≤ x < 113°
Explanation
Use your calculator in degree mode for each value of x.