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 \(0^o \leq x \leq 300^o\)
(c) Use the graph to find the value(s) of x for which:
(i) 2 cos x – sin x = 1;
(ii) tan x = 2.
Explanation
a) Table
\[\begin{array}{c|c} x & 0^o & 30^o & 60^o & 90^o & 120^o & 150^o & 180^o & 210^o & 240^o & 270^o& 300^o \\ \hline Y & 2.00 & 1.23 & 0.13 & -1.00 & -1.87 & -2.23 & -2.00 & -1.23 & -0.13 & 1.00 &1.87 \end{array}\]
(b)(i) The value of x for which 2 cos x - sinx = 1
x = \((36 \pm 3)^o\) or \((270 \pm 3)^o\)
(ii) The value of x for which tan x = 3
x = \((64 \pm 3)^o\) or \((244 \pm 3)^o\)