# Trigonometric Expressions test questions

### 1

What is the exact value of $$\sin 75^\circ$$?

### 2

What is the exact value of $$\cos105^\circ$$?

### 3

Given that $$a$$ is an acute angle and that $$\tan a= \frac{1}{5}$$, what is the exact value of $$\sin 2a$$?

### 4

When $$\sin (x + 2y)\cos (y - x) + \cos (x + 2y)\sin (y - x)$$ is simplified, what does it equal?

### 5

When $$\cos 7x^\circ \cos 5x^\circ + \sin 7x^\circ \sin 5x^\circ$$ is simplified, what is the answer?

### 6

If $$\sin x = \frac{2}{3}$$ and $$0 \textless x \textless \frac{\pi }{2}$$, find the exact values of $$\cos x$$ and $$\tan x$$.

### 7

When $$\cos x + \sqrt 3 \sin x$$ is expressed in the form $$k\sin (x + \alpha )$$, what are the values of $$k$$ and $$\alpha$$?

### 8

The maximum value of $$5\sin (x - 30)^\circ$$ occurs where $$x$$ equals:

### 9

What is the maximum value of $$2 + 3\sin (x + 20)^\circ$$?

### 10

Given that $$k\cos \alpha = - 1$$ and $$k\sin \alpha = 1$$, $$k \textgreater 0;\,0 \le \alpha \le 360$$, what are the values of $$k$$ and $$\alpha$$?