Free Printable SBQ

1.

Which expression is equivalent to the trigonometric expression $\frac{1-\sin^2\left(\theta\right)}{\cos\left(\theta\right)}$ ?

a)

$\sec\left(\theta\right)$

b)

$\sin\left(\theta\right)$

c)

$\cos\left(\theta\right)$

d)

$\csc\left(\theta\right)$

2.

Which expression is equivalent to the trigonometric expression $\sin\left(\theta\right)\cdot\sec\left(\theta\right)$ ?

a)

$\cot\left(\theta\right)$

b)

$1$

c)

$\csc\left(\theta\right)$

d)

$\tan\left(\theta\right)$

3.

Which expression is equivalent to the trigonometric expression $\sin\left(\theta\right)\cdot\cot^2\left(\theta\right)\cdot\sec^2\left(\theta\right)$ ?

a)

$\sin\left(\theta\right)$

b)

$\sec\left(\theta\right)$

c)

$\csc\left(\theta\right)$

d)

$\tan\left(\theta\right)$

4.

Which expression is equivalent to the trigonometric expression $\cot\left(\theta\right)\cdot\sec\left(\theta\right)$ ?

a)

$\sec\left(\theta\right)$

b)

$1$

c)

$\csc\left(\theta\right)$

d)

$\tan\left(\theta\right)$

5.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

6.

Simplify (Hint: you will need to FOIL first)

a)

sinθ

b)

cot²θ

c)

tan²θ

d)

cos²θ

7.

*

a)

csc² x

b)

sec² x

c)

cot² x

d)

tan² x

8.

csc(90⁰-θ) =

a)

secθ

b)

sinθ

c)

cosθ

d)

tanθ

9.

cot(90⁰-θ) =

a)

tanθ

b)

sinθ

c)

cosθ

d)

secθ

10.

a)

1/cos x

b)

1

c)

cot x

d)

-1

11.

What is the value of sin210^ocos30^o - cos210^osin30^ois

a)

0

b)

-1

c)

1

d)

sin240^o

12.

Solve on the Interval [0,2π)

tan(x)+1=2

a)

0 and π

b)

3π/4 and 7π/4

c)

π/4 and 5π/4

d)

3π/4 and 5π/4

13.

a)

No solution

b)

π/3 +2πn, 5π/3 +2πn

c)

π/6 +2πn, 11π/6 +2πn

d)

2π/3 +2πn, 4π/3 +2πn

14.

csc²x = 2 is equivalent to sin²x = ½

a)

True

b)

False

15.

Solve for 0≤x≤2π

2cos²x + cosx = 0

a)

π/2, 3π/2

b)

0, π,2π

c)

2π/3, 4π/3

d)

π/3, 5π/3

16.

Solve for 0≤x≤2π

3sin²x + sinx - 4 = 0

a)

0, π

b)

π/2

c)

π/6, 5π/6

d)

3π/2

17.

Use the information about the angle θ, 0≤θ<2π to find the exact value of
sin (2θ)
1. sin θ= 3/5 , 0<θ<π/2

a)

24/7

b)

7/25

c)

24/25

d)

1/2

18.

sin2u =

a)

(sinu)(cosu)

b)

2(sinu)(cosu)

c)

(sinu)^2

d)

2(sinu)^2

19.

Only using angles available on the unit circle, find the set of angles that will add or subtract to the given angle:
$75\degree$

a)

$80\degree-5\degree$

b)

$40\degree+35\degree$

c)

$100\degree-25\degree$

d)

$30\degree+45\degree$

20.

Write the expression as the sine or cosine of a single angle:

$\cos x\cos15\degree-\sin x\sin15\degree$

a)

$\cos\left(x-15\degree\right)$

b)

$\sin\left(x-15\degree\right)$

c)

$\cos\left(x+15\degree\right)$

d)

$\sin\left(x+15\degree\right)$

21.

Write the expression as the sine or cosine of a single angle:

$\cos\left(7y\right)\cos\left(3y\right)-\sin\left(7y\right)\sin\left(3y\right)$

a)

$\cos\left(4y\right)$

b)

$\sin\left(4y\right)$

c)

$\cos\left(10y\right)$

d)

$\sin\left(10y\right)$

SBQ - G 10.2

Total questions: 21

Worksheet time: 55mins

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