Question

1) Given that cosec x + cot x = 3, evaluate the following :
(i) cosec x - cot x
(ii) cos x

2) On the same diagram, sketch the graph of Y = I 3 sin 3/2 x I and
Y = 1 + (6x/5phi) for 0 < x < 2x
Hence, state the number of solution in this interval for the equation
I 3 sin 3/2x I = 1 + (6x/5phi)

Answer 1

Solve the equation: $|3\sin 3 / 2x| = 1 + 6x / 5\pi$

Sketching on the same diagram the graphs of $y = \left|3\sin \frac{3x}{2}\right|$ and $y = 1 + \frac{6x}{\pi}$

$\left|\sin \frac{3x}{2}\right| = 1 + \frac{6x}{\pi}$

The graph of the function $y = \sin x$

The amplitude $y = 3\sin \frac{3x}{2}$ is 3

The period $y = 3\sin \frac{3x}{2}$ is

$\frac{2\pi}{\frac{3}{2}} = \frac{4\pi}{3}$

The graph of the function $y = 3\sin \frac{3x}{2}$

The graphs of the functions $y = \left|3\sin \frac{3x}{2}\right|$ and $y = 1 + \frac{6x}{\pi}$

So for $0 < x < 2$ there are 2 solutions