Free Printable 10.5 Solving Trig Equations

1.

How many solutions does the following equation have on the given interval?

$\sin x=\frac{1}{2}$ when $0\le x<2\pi$

a)

0

b)

1

c)

2

d)

4

2.

How many solutions does the following equation have on the given interval?

$\tan^2x=3$ when $0\le x<2\pi$

a)

0

b)

1

c)

2

d)

4

3.

$\cos x+\cos^2x=0$

What method would you use to solve the equation?

a)

greatest common factor

b)

cancel cosines

c)

combine like terms

d)

square roots

4.

Solve $\cos x+\cos^2x=0$ on the interval $\pi\le x<\frac{3\pi}{2}$

a)

$\frac{\pi}{2}$

b)

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

c)

$\pi$

d)

$\frac{5\pi}{4}$

5.

$\cot^2x-2\cot x+1=0$

What method would you use to solve the equation?

a)

square roots

b)

combining like terms

c)

factoring

d)

trig identities

6.

$\cot^2x-2\cot x+1=0$

Solve on the interval $\pi\le x<2\pi$

a)

$\frac{\pi}{4}$

b)

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

c)

$\frac{5\pi}{4}$

d)

$\frac{7\pi}{4}$

7.

$2\sin^2x=2$

What method would you use to solve the equation?

a)

square roots

b)

combining like terms

c)

factoring

d)

trig identities

8.

$2\sin^2x=2$

Solve the equation on the interval $0\le x<2\pi$

a)

0

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{2}$

d)

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

e)

$\pi$

9.

$2\sin x\cos x=0$

What method would you use to solve the equation?

a)

square roots

b)

combining like terms

c)

factoring

d)

trig identities

10.

$2\sin x\cos x=0$

Solve the equation on the given interval $x\in\left\{all\ real\ numbers\right\}$

a)

$0+\frac{\pi}{2}n$

b)

$0+\pi n$

c)

$\frac{\pi}{2}+2\pi n$

d)

$0+2\pi n$

11.

$2\cos^2x-\cos x=1$

What method would you use to solve the equation?

a)

cry

b)

combining like terms

c)

factoring (move the 1 first)

d)

greatest common factor

12.

$2\cos^2x-\cos x=1$

Solve on the interval $0\le x<2\pi$

a)

0

b)

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

c)

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

d)

$\pi$

e)

$\frac{\pi}{2}$

10.5 Solving Trig Equations

Total questions: 12

Worksheet time: 2hrs 0mins

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