Question

(a) Copy and complete the table of values for y=3sin(x)+7cos(x) for 0 degrees <= x <= 180 degrees.
(b) Using a scale of 2cm to 20 degrees on the x-axis and 2cm to 2 units on the y-axis, draw the graph of y=3sin(x)+7cos(x) for 0 <= x <= 180 degrees.
(c) Using the graph, find: (i) the value of y when x=150 degrees; (ii) the range of values of x for which y>0.

Accepted Answer

(a) Completed table (y = 3sin(x)+7cos(x), to 1 d.p.):
x = 0, 20, 40, 60, 80, 100, 120, 140, 160, 180 (degrees)
y = 7.0, 7.6, 7.3, 6.1, 4.2, 1.7, -0.7, -3.4, -5.6, -7.0

(For example, at x=0: y=3sin0+7cos0=0+7=7.0. At x=180: y=3sin180+7cos180=0-7=-7.0.)

(c)(i) From the graph, when x=150 degrees, y is approximately -4.6.
(c)(ii) From the graph, the range of values of x for which y>0 is approximately 0 <= x < 113 degrees.

GCE Mathematics 2022 Theory — Question 9

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