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PC_U-Substitution with Trig

Total questions: 20

Worksheet time: 40mins

Name
Class
Date
1.

Find theta.
 sin(θ)=1\sin\left(\theta\right)=-1  

a)

 θ=90°\theta=90\degree  

b)

 θ=180°\theta=180\degree  

c)

 θ=270°\theta=270\degree  

d)

 θ=0°,360°\theta=0\degree,360\degree  

2.

Find theta.
 cos(θ)=1\cos\left(\theta\right)=-1  

a)

 θ=90°\theta=90\degree  

b)

 θ=180°\theta=180\degree  

c)

 θ=270°\theta=270\degree  

d)

 θ=0°,360°\theta=0\degree,360\degree  

3.

Find theta.
 tan(θ)=1\tan\left(\theta\right)=-1  

a)

 θ=45°\theta=45\degree  

b)

 θ=135°\theta=135\degree  

c)

 θ=225°\theta=225\degree  

d)

 θ=315°\theta=315\degree  

4.

Find theta.
 tan(θ)=1\tan\left(\theta\right)=1  

a)

 θ=45°\theta=45\degree  

b)

 θ=135°\theta=135\degree  

c)

 θ=225°\theta=225\degree  

d)

 θ=315°\theta=315\degree  

5.

Find theta.
 sin(θ)=12\sin\left(\theta\right)=-\frac{1}{2}  

a)

 θ=120°\theta=120\degree  

b)

 θ=210°\theta=210\degree  

c)

 θ=330°\theta=330\degree  

d)

 θ=60°\theta=60\degree  

6.

Find theta.
 cos(θ)=12\cos\left(\theta\right)=-\frac{1}{2}  

a)

 θ=120°\theta=120\degree  

b)

 θ=210°\theta=210\degree  

c)

 θ=330°\theta=330\degree  

d)

 θ=240°\theta=240\degree  

7.

Find theta.
 sin(θ)=12\sin\left(\theta\right)=\frac{1}{2}  

a)

 θ=30°\theta=30\degree  

b)

 θ=150°\theta=150\degree  

c)

 θ=300°\theta=300\degree  

d)

 θ=60°\theta=60\degree  

8.

Find theta.
 cos(θ)=12\cos\left(\theta\right)=\frac{1}{2}  

a)

 θ=30°\theta=30\degree  

b)

 θ=150°\theta=150\degree  

c)

 θ=300°\theta=300\degree  

d)

 θ=60°\theta=60\degree  

9.

Which is the correct use of u-substitution for the trig equation?
 2sin2x+sinx=2sinx32\sin^2x+\sin x=2\sin x-3  

a)

 u22u+3=0u^2-2u+3=0  

b)

 2u2u3=02u^2-u-3=0  

c)

 2u2+u3=02u^2+u-3=0  

d)

 2u2u+3=02u^2-u+3=0  

10.

Which is the correct use of u-substitution for the trig equation?
 2cos2x+cosx=2cosx12\cos^2x+\cos x=2\cos x-1  

a)

 u22u+1=0u^2-2u+1=0  

b)

 2u2u1=02u^2-u-1=0  

c)

 2u2+u1=02u^2+u-1=0  

d)

 2u2u+1=02u^2-u+1=0  

11.

Which is the correct use of u-substitution for the trig equation?
 2sin2x+3sinx=sin2x+12\sin^2x+3\sin x=\sin^2x+1  

a)

 u23u1=0u^2-3u-1=0  

b)

 u2+3u1=0u^2+3u-1=0  

c)

 u2+3u+1=0u^2+3u+1=0  

d)

 2u2+3u1=02u^2+3u-1=0  

12.

Which is the correct use of u-substitution for the trig equation?
 2cos2x+cosx=3cos2x+12\cos^2x+\cos x=3\cos^2x+1  

a)

 0=u2u+10=u^2-u+1  

b)

 0=2u2u+10=2u^2-u+1  

c)

 0=u2+u10=u^2+u-1  

d)

 0=u2+u+10=u^2+u+1  

13.

Which is the correct use of u-substitution for the trig equation?
 2tan2x+3tanx=3tan2x+52\tan^2x+3\tan x=3\tan^2x+5  

a)

 0=u23u+50=u^2-3u+5  

b)

 0=3u2u+50=3u^2-u+5  

c)

 0=3u22u+50=3u^2-2u+5  

d)

 0=u2+3u50=u^2+3u-5  

14.

Which is the correct use of u-substitution for the trig equation?
 3tan2x+3tanx=2tan2x+53\tan^2x+3\tan x=2\tan^2x+5  

a)

 u2+3u+5=0u^2+3u+5=0  

b)

 u23u+5=0u^2-3u+5=0  

c)

 3u2+u5=03u^2+u-5=0  

d)

 u2+3u5=0u^2+3u-5=0  

15.

 Factor:
 x25x14x^2-5x-14 

a)

 (x2)(x+3)(x-2)(x+3)  

b)

 (x2)(x+7)(x-2)(x+7)  

c)

 (x+2)(x7)(x+2)(x-7)  

d)

 (x2)(x3)(x-2)(x-3)  

16.

Factor
 x22x15x^2-2x-15  


a)

 (x+5)(x3)(x+5)(x-3)  

b)

 (x5)(x3)(x-5)(x-3)  

c)

 (x5)(x+3)(x-5)(x+3)  

d)

 (x+5)(x+3)(x+5)(x+3)  

17.

Factor
 x2+7x+12x^2+7x+12  


a)

 (x+2)(x+10)(x+2)(x+10)  

b)

 (x+3)(x+4)(x+3)(x+4)  

c)

 (x+4)(x+5)(x+4)(x+5)  

d)

 (x+4)(x+6)(x+4)(x+6)  

18.

Factor:
 x2+7x30x^2+7x-30  

a)

 (x+10)(x7)(x+10)(x-7)  

b)

 (x10)(x+3)(x-10)(x+3)  

c)

 (x+10)(x+3)(x+10)(x+3)  

d)

 (x+10)(x3)(x+10)(x-3)  

19.

Factor
 x2+9x36x^2+9x-36  

a)

 (x+12)(x3)(x+12)(x-3)  

b)

 (x+9)(x4)(x+9)(x-4)  

c)

 (x12)(x+3)(x-12)(x+3)  

d)

 (x9)(x4)(x-9)(x-4)  

20.

Factor:
 x215x+36x^2-15x+36  

a)

 (x18)(x+2)(x-18)(x+2)  

b)

 (x12)(x3)(x-12)(x-3)  

c)

 (x12)(x+3)(x-12)(x+3)  

d)

 (x+18)(x2)(x+18)(x-2)