Theory question 112
Trigonometry(a) Copy and complete the table of values for y = 1 − 4 cos x.
x: 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°
y: −3.0, __, __, 1.0, __, __, __, 4.5, __, __, −1.0
(b) Using a scale of 2 cm to 30° on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of y = 1 − 4 cos x for 0° ≤ x ≤ 300°.
(c) Use the graph to: (i) solve the equation 1 − 4 cos x = 0; (ii) find the value of y when x = 105°; (iii) find x when y = 1.5.
Show the model answer
(a) 30°: −2.5; 60°: −1.0; 120°: 3.0; 150°: 4.5; 180°: 5.0; 240°: 3.0; 270°: 1.0.
(b) Plot the points and draw a smooth curve.
(c)(i) Where the curve crosses the x-axis: x ≈ 76° and x ≈ 284°.
(ii) At x = 105°, y ≈ 2.0.
(iii) Where y = 1.5: x ≈ 97° and x ≈ 263°.
(Accept graph readings within about ±2°.)
For example at 30°: 1 − 4(0.866) = −2.46 ≈ −2.5.