a) Copy and complete the following table of values... | WAEC SSCE - General Mathematics - 2018 (Essay)

Question 1 Report

a) Copy and complete the following table of values for y = 2 cos x – sin x ,\(0^o \leq x \leq 300^o\)

\[\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\ \hline Y & 2.00 & & 0.13 & & -1.87 & & -2.00 & & -0.13 & & \end{array}\]

(b) Using scales of 2 cm to 30\(^o\) on the x-axis and 2cm to 1 unit on the y-axis, draw the graph of y = 2 cos x – sin x for \(0^o \leq x \leq 300^o\)

(i) 2 cos x – sin x = 1;

(ii) tan x = 2.

Answer

(a) Completed table for \(y=2\cos x-\sin x\):

\(x\)	\(0^\circ\)	\(30^\circ\)	\(60^\circ\)	\(90^\circ\)	\(120^\circ\)	\(150^\circ\)	\(180^\circ\)	\(210^\circ\)	\(240^\circ\)	\(270^\circ\)	\(300^\circ\)
\(y\)	2.00	1.23	0.13	-1.00	-1.87	-2.23	-2.00	-1.23	-0.13	1.00	1.87

For example, at \(x=30^\circ\):

\[y=2\cos30^\circ-\sin30^\circ=2(0.866)-0.5=1.232\ldots\approx1.23.\]

(b) Graph of \(y=2\cos x-\sin x\)

(c)(i) To solve \(2\cos x-\sin x=1\), draw or imagine the horizontal line \(y=1\). The required values are the \(x\)-coordinates where this line meets the curve:

\[x\approx36^\circ\quad\text{or}\quad x\approx270^\circ.\]

(c)(ii) Since

\[\tan x=2 \quad\Rightarrow\quad \frac{\sin x}{\cos x}=2 \quad\Rightarrow\quad \sin x=2\cos x,\]

this is equivalent to

\[2\cos x-\sin x=0.\]

Therefore, read the \(x\)-coordinates where the curve crosses the \(x\)-axis:

\[x\approx63^\circ\quad\text{or}\quad x\approx243^\circ.\]

Examination reminder: For an equation involving \(2\cos x-\sin x\), use the graph’s \(y\)-value. In particular, \(\tan x=2\) rearranges to \(2\cos x-\sin x=0\), so look for the \(x\)-intercepts of the curve.

Read lesson note on Trigonometry (JAMB)

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Read lesson note on Progression (JAMB)

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