Free Printable Solving Trig Equations

1.

Why doesn't 2cosx − 3 = 0 have solutions?

a)

cos x is never bigger than one

b)

cos x is never equal to a fraction

c)

Actually, this equation does have a solution, x = π

d)

This equation will have a solution tomorrow.

2.

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

a)

-cos²x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

3.

Choose a good way to start solving this equation

tanx sin²x = 2 tanx

a)

divide tanx from both sides

b)

factor out tanx

c)

subtract 2 tanx from the left and then factor tanx out

d)

cancel sin²x out

4.

Factor 0 = sin²x − sinx

a)

0 = sinx(sinx)

b)

0 = sinx(1 − sinx)

c)

0 = cosx(sinx − 1)

d)

0 = sinx(sinx − 1)

5.

Factor: sec²x − secx − 2

a)

(sec x)(secx − 2)

b)

(secx − 2)(secx − 1)

c)

(secx − 2)(secx + 1)

d)

(secx + 2)(secx − 1)

6.

To solve the equation sec²x − secx = 2

a)

start by subtracting 2 from both sides and then factor

b)

add sec x to both sides and factor

c)

factor out secx and set each factor equal to 2

d)

sec x is never bigger than 1, so there are no solutions

7.

csc²x = 2 is equivalent to sin²x = ½

a)

True

b)

False

8.

Solve equation for $0\le\theta<2\pi$ .
$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

9.

Solve for all values of x over the interval [0,2π]

a)

$\frac{\pi}{6}\ and\ \frac{7\pi}{6}$

b)

$\frac{5\pi}{6}\ and\ \frac{11\pi}{6}$

c)

$\frac{\pi}{3}\ and\ \frac{5\pi}{3}$

d)

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

10.

Solve equation for $0\le\theta<2\pi$ .
$-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$

a)

$\theta=\frac{5\pi}{4},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{6},\frac{7\pi}{4}$

c)

$\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{5\pi}{4},\frac{7\pi}{4}$

11.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta=7\sin^2\theta+4\sin\theta+1$

a)

$\theta=\frac{7\pi}{6}$

b)

$\theta=0,\frac{\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{7\pi}{6},\frac{11\pi}{6}$

12.

Solve equation for $0\le\theta<2\pi$ .
$\sec^2\theta+3=2\sec\theta+2$

a)

$\theta=0,\frac{\pi}{2},\frac{2\pi}{3},\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{3},\pi,\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{4}$

d)

$\theta=0$

13.

Solve for all values of x over the interval [0,2π]

a)

$\frac{3π}{4}and\ \frac{5π}{4}\$

b)

$\frac{π}{4}and\ \frac{3π}{4}$

c)

$\frac{π}{4},\frac{3π}{4},\frac{5π}{4}\ and\ \frac{7π}{4}$

d)

$\frac{\pi}{6}\ and\ \frac{5\pi}{6}$

14.

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

a)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

15.

Solve equation for $0\le\theta<2\pi$ .
$2+3\csc\theta+2\csc^2\theta=\csc^2\theta$

a)

$\theta=\frac{3\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

d)

$\theta=\frac{\pi}{4},\frac{11\pi}{6}$

16.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\pi$

17.

$2\cos^2x-3\cos\left(x\right)+1=0$ Solve on the interval $\left[0,2\pi\right]$

a)

$x=0,\frac{\pi}{3},\frac{5\pi}{3},2\pi$

b)

$x=\frac{\pi}{6},\frac{\pi}{2},\frac{11}{6}$

c)

$x=0,\pi,2\pi$

d)

$x=\frac{\pi}{6},\frac{\pi}{2},\frac{5\pi}{6}$

18.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

19.

Find all solutions on the interval $\left[0,\ 2\pi\right)$ for $\sec^2x\ -\ 1=0$

a)

$x=0,\ \ \ x=\pi$

b)

$x=\frac{\pi}{2},\ \ \ x=\frac{3\pi}{2}$

c)

$x=\frac{\pi}{4},\ \ \ x=\frac{3\pi}{4}$

d)

$x=0$

20.

Solve for all values of x over the interval [0,2π] : $\tan^{2\ }x\ -2\ \tan x\ =-1$

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

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

Solving Trig Equations - Extra Time

Total questions: 20

Worksheet time: 3hrs 30mins

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