Question

9(a) Copy and complete the table of values for y=3sinx+7cosx for 0°≤x≤180°.
(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=3sinx+7cosx for 0<x<180°.
(c) Using the graph, find: (i) value of y when x=150°; (ii) range of values of x for which y>0.

Accepted Answer

(a) Completed table (x in degrees, y=3sinx+7cosx):
x: 0°, 20°, 40°, 60°, 80°, 100°, 120°, 140°, 160°, 180°
y: 7.0, 7.6, 7.3, 6.1, 4.2, 1.7, −0.9, −3.1, −5.6, −7.0

(b) [Graph plotted from the table of values above, using the given scale, showing a smooth curve decreasing from y=7 at x=0° through zero around x≈113° down to y=−7 at x=180°.]

(c)(i) From the graph, the value of y when x=150° is y=−4.4.
(ii) Range of values of x for which y>0: {x: 0°<x<113°}.

WAEC Mathematics 2022 Theory — Question 9

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