Systems of Trigonometric Equations

Practice Questions

Trigonometry › Systems of Trigonometric Equations

Questions

10

1

For this question, we will denote by max the maximum value of the function and min the minimum value of the function.

What is the maximum and minimum values of

where is a real number.

2

Find the values of that satisfy the following system:

$\left{\begin{matrix} 2cosx\le \sqrt{2}\2sinx\le \sqrt{2} \ cosx< sinx\end{matrix}\right.$

where is assumed to be $[0,\frac{\pi}{2}]$

3

Which of the following systems of trigonometric equations have a solution with an -coordinate of $\frac{\pi}{4}$ ?

4

Solve the system for $\theta$ :

$\begin{matrix} y = 6 \sin \theta - 1 \ y = \sin ^2 \theta + 4 \end{matrix}$

5

Solve this system for $\theta$ :

$\begin{matrix} y = \sin ^2 \theta + 1 \ y = \cos \theta + 2 \end{matrix}$

6

Solve this system for $\theta$ :

$\begin{matrix} y = 5 \sin (\frac{ \theta }{2}) + 3 \ y = 3 \sin (\frac{\theta }{2} ) + 2 \end{matrix}$

7

Solve this system for $\theta$ :

$y = \sin ^ 2 \theta + \cos \theta$

$y = \cos \theta + \frac{1}{2}$

8

Solve this system for $\theta$ :

$\ y = \cos ^2 \theta + \frac{1}{2} \ y = \sin ^2 \theta$

9

Solve this system for $\theta$ :

$\y = 4 \cos ^ 2 \theta + \cos \theta - 5 \ y = \cos \theta - 2$

10

Solve the following system:

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