(a) Copy and complete the table of values for \(y = 3\sin x + 2\cos x\) for \(0° \leq x \leq 360°\). x 0° 60° 120° 180° 240° 300° 360° y 2.00 2.00 (b) Using...
Question 1 Report
(a) Copy and complete the table of values for \(y = 3\sin x + 2\cos x\) for \(0° \leq x \leq 360°\).
| x | 0° | 60° | 120° | 180° | 240° | 300° | 360° |
| y | 2.00 | 2.00 |
(b) Using a scale of 2 cm to 60° on x- axis and 2 cm to 1 unit on the y- axis, draw the graph of \(y = 3 \sin x + 2 \cos x\) for \(0° \leq x \leq 360°\).
(c) Use your graph to solve the equation : \(3 \sin x + 2 \cos x = 1.5\).
(d) Find the range of values of x for which \(3\sin x + 2\cos x < -1\).
Answer Details
(a) For \(y=3\sin x+2\cos x\), the completed table is:
| \(x\) | \(0^\circ\) | \(60^\circ\) | \(120^\circ\) | \(180^\circ\) | \(240^\circ\) | \(300^\circ\) | \(360^\circ\) |
|---|---|---|---|---|---|---|---|
| \(y\) | 2.00 | 3.60 | 1.60 | -2.00 | -3.60 | -1.60 | 2.00 |
For example, at \(x=60^\circ\), \(y=3(0.8660)+2(0.5)=3.598\approx3.60\).
(b) The graph, drawn using the stated scales, is shown below.
(c) Draw the horizontal line \(y=1.5\). Its intersections with the curve give
\[x\approx122^\circ\quad\text{or}\quad x\approx351^\circ.\]
(d) Draw the horizontal line \(y=-1\). The curve is below this line between its two points of intersection. Hence,
\[\boxed{162^\circ<x<310^\circ}.\]
Download The App On Google Playstore
Everything you need to excel in your exams
