Question

9(a). Copy and complete the table of values for y = 2cosx + 3sinx for 0° ≤ x° ≤ 360°.
x: 0°, 60°, 120°, 180°, 240°, 300°, 360°
(b) Using a scale of 2cm to 60° on the x-axis and 2cm to 1 unit on the y-axis, draw the graph of y = 2cosx + 3sinx for 0° ≤ x° ≤ 360°.
(c) Using the graph to: (i) solve 2cosx + 3sinx = −1; (ii) find, correct to one decimal place, the value of y when x = 342°.

Accepted Answer

(a) Completed table (x, y=2cosx+3sinx): x=0°→y=2.0; x=60°→y=2.6; x=120°→y=1.6; x=180°→y=−2.0; x=240°→y=−3.6; x=300°→y=−2.6; x=360°→y=2.0.

(b) The graph of y=2cosx+3sinx is a sinusoidal curve, plotted using the table of values from (a), starting and ending near y=2 at x=0° and x=360°, dipping to a minimum around x=240°.

(c)(i) Since y=2cosx+3sinx, setting y=−1 and tracing on the graph, the solutions are x ≈ 162° and x ≈ 312°.
(ii) When x=342°, tracing on the graph, y ≈ 0.9.

WAEC Mathematics 2019 Theory — Question 11

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