(a) Copy and complete the table of values for the relation \(y = 2 \sin x + 1\) x 0° 30° 60° 90° 120° 150° 180° 210° 240° 270° y 1.0 2.7 0.0 -0.7 (b) Using ...
Question 1 Report
(a) Copy and complete the table of values for the relation \(y = 2 \sin x + 1\)
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° | 270° |
| y | 1.0 | 2.7 | 0.0 | -0.7 |
(b) Using scales of 2 cm to 30° on the x- axis and 2 cm to 1 unit on the y- axis, draw the graph of \(y = 2 \sin x + 1, 0° \leq x \leq 270°\).
(c) Use the graph to find the values of x for which \(\sin x = \frac{1}{4}\).
Answer Details
(a) For \(y=2\sin x+1\), the completed table is:
| \(x\) | \(0^\circ\) | \(30^\circ\) | \(60^\circ\) | \(90^\circ\) | \(120^\circ\) | \(150^\circ\) | \(180^\circ\) | \(210^\circ\) | \(240^\circ\) | \(270^\circ\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(y\) | 1.0 | 2.0 | 2.7 | 3.0 | 2.7 | 2.0 | 1.0 | 0.0 | -0.7 | -1.0 |
For example, \(y(60^\circ)=2\sin60^\circ+1=2(0.866)+1\approx2.7\).
(b) The required graph, plotted using the stated scales, is shown below.
(c) If \(\sin x=\frac14\), then
\[y=2\sin x+1=2\left(\frac14\right)+1=1.5.\]
Draw the horizontal line \(y=1.5\) and read its two points of intersection with the curve. Hence,
\[\boxed{x\approx15^\circ\text{ or }168^\circ}.\]
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