Theory question 112
Trigonometry(a) Copy and complete the table of values for y = 3 sin x + 2 cos x for 0° ≤ x ≤ 360°.
x: 0°, 60°, 120°, 180°, 240°, 300°, 360°
y: 2.00, –, –, –, –, –, 2.00
(b) Using a scale of 2 cm to 60° on x-axis and 2 cm to 1 unit on y-axis, draw the graph of y = 3 sin x + 2 cos x for 0° ≤ x ≤ 360°.
(c) Use your graph to solve the equation: 3 sin x + 2 cos x = 1.5.
(d) Find the range of values of x for which 3 sin x + 2 cos x < −1.
Show the model answer
(a) 0°: 2.00; 60°: 3.60; 120°: 1.60; 180°: −2.00; 240°: −3.60; 300°: −1.60; 360°: 2.00.
(b) Plot the points and join with a smooth curve.
(c) Where y = 1.5 meets the curve: x ≈ 122° and x ≈ 351°.
(d) The curve is below y = −1 for about 162° < x < 310°.
(Accept graph readings within a few degrees.)
For example at 60°: 3(0.866) + 2(0.5) = 3.60.