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Solving Trig Equations

Total questions: 10

Worksheet time: 5mins

Name
Class
Date
1.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 4+6cos⁡θ=74+6\cos\theta=7  

a)

 θ=π3 or 5π3\theta=\frac{\pi}{3}\ or\ \frac{5\pi}{3}  

b)

 θ=π6 or 11π6\theta=\frac{\pi}{6}\ or\ \frac{11\pi}{6}  

c)

 θ=π6 or 5π6\theta=\frac{\pi}{6}\ or\ \frac{5\pi}{6}  

d)

 θ=π3 or 2π3\theta=\frac{\pi}{3}\ or\ \frac{2\pi}{3}  

2.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 4+6cos⁡θ=14+6\cos\theta=1  

a)

 θ=2π3 or 4π3\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}  

b)

 θ=5π6 or 7π6\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}  

c)

 θ=π3 or 2π3\theta=\frac{\pi}{3}\ or\ \frac{2\pi}{3}  

d)

 θ=7π6 or 11π6\theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6}  

3.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 7−2sin⁡θ=67-\sqrt{2}\sin\theta=6  

a)

 θ=π4 or 3π4\theta=\frac{\pi}{4}\ or\ \frac{3\pi}{4}  

b)

 θ=π2 or 3π2\theta=\frac{\pi}{2}\ or\ \frac{3\pi}{2}  

c)

 θ=π4 or 7π4\theta=\frac{\pi}{4}\ or\ \frac{7\pi}{4}  

d)

 θ=5π4 or 7π4\theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4}  

4.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 −1+3tan⁡θ=2-1+\sqrt{3}\tan\theta=2  

a)

 θ=π3 or 4π3\theta=\frac{\pi}{3}\ or\ \frac{4\pi}{3}  

b)

 θ=π3 or 5π3\theta=\frac{\pi}{3}\ or\ \frac{5\pi}{3}  

c)

 θ=π6 or 5π6\theta=\frac{\pi}{6}\ or\ \frac{5\pi}{6}  

d)

 θ=π6 or 7π6\theta=\frac{\pi}{6}\ or\ \frac{7\pi}{6}  

5.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 3sin⁡θ=−32\sqrt{3}\sin\theta=-\frac{3}{2}  

a)

 θ=4π3 or 5π3\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}  

b)

 θ=7π6 or 11π6\theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6}  

c)

 θ=2π3 or 4π3\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}  

d)

 θ=5π6 or 7π6\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}  

6.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 3cos⁡θ+4.5=3\sqrt{3}\cos\theta+4.5=3  

a)

 θ=4π3 or 5π3\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}  

b)

 θ=7π6 or 11π6\theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6}  

c)

 θ=2π3 or 4π3\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}  

d)

 θ=5π6 or 7π6\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}  

7.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 2tan⁡θ+7=52\tan\theta+7=5  

a)

 θ=3π4 or 7π4\theta=\frac{3\pi}{4}\ or\ \frac{7\pi}{4}  

b)

 θ=3π4 or 5π4\theta=\frac{3\pi}{4}\ or\ \frac{5\pi}{4}  

c)

 θ=π4 or 5π4\theta=\frac{\pi}{4}\ or\ \frac{5\pi}{4}  

d)

 θ=5π4 or 7π4\theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4}  

8.

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 2cos⁡θ=−22\cos\theta=-\sqrt{2} 

a)

θ=3π4 or 7π4\theta=\frac{3\pi}{4}\ or\ \frac{7\pi}{4}

b)

θ=3π4 or 5π4\theta=\frac{3\pi}{4}\ or\ \frac{5\pi}{4}

c)

θ=π4 or 5π4\theta=\frac{\pi}{4}\ or\ \frac{5\pi}{4}

d)

θ=5π4 or 7π4\theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4}

9.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 12sin⁡θ+7=112\sin\theta+7=1  

a)

 θ=4π3 or 5π3\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}  

b)

 θ=7π6 or 11π6\theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6}  

c)

 θ=2π3 or 4π3\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}  

d)

 θ=5π6 or 7π6\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}  

10.

Solve for  θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right) :

 3tan⁡x+5=4\sqrt{3}\tan x+5=4  

a)

 θ=4π3 or 5π3\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}  

b)

 θ=7π6 or 11π6\theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6}  

c)

 θ=π3 or 4π3\theta=\frac{\pi}{3}\ or\ \frac{4\pi}{3}  

d)

 θ=5π6 or 11π6\theta=\frac{5\pi}{6}\ or\ \frac{11\pi}{6}  

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