Free Printable Pre-Calc - Sum/Diff Identities & Simplifying Trig Expressions

1.

Use Sum or Difference Identities to find the exact value of each expression.
cos(75°)

a)

1/4

b)

√6/4 - √2 / 4

c)

√6 + √2 / 4

d)

-√6/4 - √2 / 4

2.

Expand and simplify $\cos\ \left(90^o-x\right)$

a)

$\cos\ x$

b)

$\sin\ x$

c)

$\tan\ x$

d)

$-\cos x$

3.

Use sum or difference angles identity to find the exact value for $\cos105^o$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{-\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

4.

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$-\frac{\sqrt{3}}{2}$

5.

Find the exact value of the expression.
cos(20)cos(40) - sin(20)sin(40)

a)

1/4

b)

1/2

c)

√(3)/2

d)

√(3)

6.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

7.

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

a)

sin(120)

b)

cos(120)

c)

cos(230)

d)

sin(230)

8.

Which is equivalent to $\sin30\cos60+\cos30\sin60$

a)

$\sin90$

b)

$\sin30$

c)

$\cos90$

d)

$\cos30$

9.

Which is equivalent to $\sin100\cos20-\cos100\sin20$

a)

$\sin120$

b)

$\sin80$

c)

$\cos120$

d)

$\cos80$

10.

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

$\sin\left(\frac{\pi}{5}\right)\cos\left(\frac{\pi}{2}\right)+\sin\left(\frac{\pi}{2}\right)\cos\left(\frac{\pi}{5}\right)$

a)

$\cos\left(\frac{3\pi}{10}\right)$

b)

$\sin\left(\frac{3\pi}{10}\right)$

c)

$\cos\left(\frac{7\pi}{10}\right)$

d)

$\sin\left(\frac{7\pi}{10}\right)$

11.

Reduce the expression.

a)

$\cos u$

b)

$-\sin x$

c)

$\sin u$

d)

$\cos x$

12.

Simplify the trig expression.

a)

sinx

b)

cosx

c)

cotx

d)

tanx

13.

Simplify the trig expression.

a)

1

b)

-tanx

c)

-1

d)

tanx

14.

Simplify the trig expression.

a)

tan²x

b)

2

c)

cot²x

d)

1

15.

Simplify the trig expression.

a)

secx

b)

cotx

c)

sec²x

d)

tan²x

16.

a)

csc x

b)

sec x

c)

1/sec x

d)

cos x

17.

a)

csc x

b)

1/sec x

c)

1 + sec x

d)

sec x

18.

a)

sin x

b)

cos x

c)

tan x

d)

1

19.

Simplify the trig expression.

a)

secx

b)

cotx

c)

sec²x

d)

tan²x

20.

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

Pre-Calc - Sum/Diff Identities & Simplifying Trig Expressions

Total questions: 20

Worksheet time: 4hrs 55mins

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