Theory question 108
Trigonometry(a) Copy and complete the table for the relation y = 2 cos 2x − 1
x: 0°, 30°, 60°, 90°, 120°, 150°, 180°
y = 2cos 2x − 1: 10, 0, __, __, __, __, 1.0
(b) Using a scale of 2 cm = 30° on the x-axis and 2cm = 1 unit on the y-axis, draw the graph of y = 2 cos 2x − 1 for 0° ≤ x ≤ 180°
(c) On the same axis draw the graph of y = 1/180 (x − 360).
(d) Use your graphs to find the: (i) values of x for which 2 cos 2x + ½ = 0; (ii) roots of the equation 2 cos 2x − x/180 + 1 = 0.
Show the model answer
(a) x = 0°: 1.0; 30°: 0; 60°: −2; 90°: −3; 120°: −2; 150°: 0; 180°: 1.0
(b) Plot the points and join with a smooth curve.
(c) Straight line through (0°, −2) and (180°, −1).
(d)(i) 2 cos 2x + ½ = 0 means 2 cos 2x − 1 = −1½: draw y = −1½ and read x ≈ 52° and x ≈ 128°
(ii) The equation rearranges to 2 cos 2x − 1 = (x − 360)/180, so read where the curve meets the line: x ≈ 55° and x ≈ 131°
Rearrange each equation so one side is the plotted curve; the other side gives the line to draw.