(a) Copy and complete the table of values for \(y = \sin x + 2 \cos x\), correct to one decimal place. x 0° 30° 60° 90° 120° 150° 180° 210° 240° y 2.2 -1.2 ...
Question 1 Report
(a) Copy and complete the table of values for \(y = \sin x + 2 \cos x\), correct to one decimal place.
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° |
| y | 2.2 | -1.2 | -2.0 | -1.9 |
(b) Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 units on the y- axis, draw the graph of \(y = \sin x + 2\cos x\) for \(0° \leq x \leq 240°\).
(c) Use your graph to solve the equation : (i) \(\sin x + 2 \cos x = 0\) ; (ii) \(\sin x = 2.1 - 2\cos x\).
(d) From the graph, find y when x = 171°.
Answer Details
(a) For each value of x, evaluate \(y=\sin x+2\cos x\), correct to one decimal place.
| \(x\) | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° |
|---|---|---|---|---|---|---|---|---|---|
| \(y\) | 2.0 | 2.2 | 1.9 | 1.0 | −0.1 | −1.2 | −2.0 | −2.2 | −1.9 |
(b) The plotted graph is shown below. The points are joined with a smooth curve.
(c)
(i) The x-intercept of the curve gives
\[x\approx117^\circ.\]
(ii) Draw the horizontal line \(y=2.1\). Its intersections with the curve give
\[x\approx9^\circ\quad\text{or}\quad x\approx45^\circ.\]
(d) Reading the ordinate at \(x=171^\circ\) from the graph gives
\[y\approx-1.75.\]
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