- In this question you should show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
- Solve, for \(0 < \theta \leqslant 450 ^ { \circ }\), the equation
$$5 \cos ^ { 2 } \theta = 6 \sin \theta$$
giving your answers to one decimal place.
- (a) A student's attempt to solve the question
"Solve, for \(- 90 ^ { \circ } < x < 90 ^ { \circ }\), the equation \(3 \tan x - 5 \sin x = 0\) " is set out below.
$$\begin{gathered}
3 \tan x - 5 \sin x = 0
3 \frac { \sin x } { \cos x } - 5 \sin x = 0
3 \sin x - 5 \sin x \cos x = 0
3 - 5 \cos x = 0
\cos x = \frac { 3 } { 5 }
x = 53.1 ^ { \circ }
\end{gathered}$$
Identify two errors or omissions made by this student, giving a brief explanation of each.
The first four positive solutions, in order of size, of the equation
$$\cos \left( 5 \alpha + 40 ^ { \circ } \right) = \frac { 3 } { 5 }$$
are \(\alpha _ { 1 } , \alpha _ { 2 } , \alpha _ { 3 }\) and \(\alpha _ { 4 }\)
(b) Find, to the nearest degree, the value of \(\alpha _ { 4 }\)