Solve Trigonometric Equations and Inequalities

Practice Questions

Pre-Calculus › Solve Trigonometric Equations and Inequalities

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1

Find $\sin\bigg(\frac{\pi }{3} + \frac{\pi }{6}\bigg)$ using the sum identity.

2

Evaluate

$\sin \left(\frac{5 \pi}{12}\right)$ .

3

Find the value of .

4

In the problem below, $\sin \alpha = \frac {1}{5}, 0 < \alpha < \frac {\pi}{2}$ and $\cos \beta = \frac {1}{4}, 0 < \beta< \frac {\pi}{2}$ .

Find

$\sin (\alpha + \beta)$ .

5

Given that $\tan x = 2$ and $\tan y = 3$ , find $\tan (x+y)$ .

6

In the problem below, $\sin \alpha = \frac {1}{5}, 0 < \alpha < \frac {\pi}{2}$ and $\cos \beta = \frac {1}{4}, 0 < \beta< \frac {\pi}{2}$ .

Find

$\cos (\alpha - \beta)$ .

7

Calculate $\sin(75)$ .

8

Use trigonometric identities to solve the equation for the angle value.

$4\cos^2\theta+\cos{2\theta}+\sin^2\theta=3$

9

Use trigonometric identities to solve the following equation for $\theta$ :

$tan^2\theta + sec^2\theta = 1$

10

Find one possible value of .

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