Quiz about Trig Identities

Question 1

Please select the correct solution

Accepted Answer

sec2 x

Answer

csc2 x

Answer

cot2 x

Answer

sin2 x

Question 2

Please select the correct solution
cos²x + sin ²x=

Accepted Answer

1

Answer

csc²x + sec²x

Answer

sin 2 x

Answer

1 - sin 2 x

Question 3

Please select the correct solution

Accepted Answer

tan x

Answer

csc x

Answer

sec x

Answer

cot x

Question 4

Simplify: tanxcotx-cos²x

Accepted Answer

sin2x

Answer

tanx

Answer

cotx

Answer

cos2x

Question 5

Simplify
(sec x)(cot x)(sin x)

Accepted Answer

1

Answer

sin x

Answer

- sin x

Answer

-1

Question 6

Question 6.

Accepted Answer

1

Answer

1/cos x

Answer

cot x

Answer

-1

Question 7

Select all that are Pythagorean Identities.

Accepted Answer

sin²(u) + cos²(u) = 1

Accepted Answer

tan²(u) + 1 = sec²(u)

Accepted Answer

cot²(u) + 1 = csc²(u)

Answer

sin²(u) - cos²(u) = 1

Answer

cot²(u) + csc²(u) = 1

Question 8

Simplify.

Accepted Answer

cos x

Answer

sin x

Answer

tan x

Answer

1

Question 9

The expression sinx(secx-cscx) is equivalent to:

Accepted Answer

tanx-1

Answer

1-tanx

Answer

1-cotx

Answer

sinx

Question 10

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

Accepted Answer

cos(120)

Answer

sin(120)

Answer

cos(230)

Answer

sin(230)

Question 11

Question 11.

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 12

Question 12.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 13

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

Accepted Answer

120/169

Answer

25/169

Answer

60/169

Answer

5/13

Question 14

Assume A and B are positive acute angles. If sinA=15/17 and cosB=4/5, find the cos(A - B).

Accepted Answer

77/85

Answer

3/8

Answer

8/17

Answer

-13/85

Question 15

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

Accepted Answer

120/169

Answer

25/169

Answer

60/169

Answer

5/13

Question 16

Accepted Answer

$$\frac{4\sqrt{2}}{9}$$

Answer

$$\frac{2}{3}$$

Answer

$$\frac{4\sqrt{2}}{3}$$

Answer

$$\frac{\sqrt{2}-\sqrt{6}}{3}$$

Question 17

$$If\ \sin heta\ =\ \frac{4}{5},\ where\ 0\le heta\le\frac{\pi}{2},find\ \sin2 heta$$

Accepted Answer

$$\frac{24}{25}$$

Answer

$$\frac{12}{25}$$

Answer

$$-\frac{24}{25}$$

Answer

$$\frac{3}{5}$$

Question 18

$$If\ \sin heta\ =\ \frac{-4}{5},\ where\ \pi\le heta\le\frac{3\pi}{2},find\ \sin2 heta$$

Accepted Answer

$$\frac{24}{25}$$

Answer

$$\frac{12}{25}$$

Answer

$$-\frac{24}{25}$$

Answer

$$\frac{3}{5}$$

Question 19

$$If\ \sin heta\ =\ \frac{4}{5},\ where\ \frac{\pi}{2}\le heta\le\pi,find\ \cos2 heta$$

Accepted Answer

$$\frac{-7}{25}$$

Answer

$$\frac{7}{25}$$

Answer

$$\frac{24}{25}$$

Answer

$$-\frac{24}{25}$$

Question 20

$$If\ \sin heta\ =\ \frac{4}{5},\ where\ \frac{\pi}{2}\le heta\le\pi,find\ \sin2 heta$$

Accepted Answer

$$-\frac{24}{25}$$

Answer

$$\frac{7}{25}$$

Answer

$$\frac{24}{25}$$

Answer

$$\frac{-7}{25}$$

Question 21

$$If\ an heta\ =\ \frac{-4}{3},\ where\ \frac{3\pi}{2}\le heta\le2\pi,find\ \sin2 heta$$

Accepted Answer

$$-\frac{24}{25}$$

Answer

$$\frac{7}{25}$$

Answer

$$\frac{24}{25}$$

Answer

$$\frac{-7}{25}$$

Question 22

$$\cos70^o\cos40^o-\sin70^o\sin40^o\ $$ is equivalent to

Accepted Answer

$$\cos110^o$$

Answer

$$\cos30^o$$

Answer

$$\cos70^{o\ }$$

Answer

$$\sin70^{o\ }$$

Question 23

If $$\sin A=\frac{4}{5}, an B=\frac{5}{12},$$ and A and B are first quadrant angles, what is the value of $$\sin\left(A+B ight)$$ ?

Accepted Answer

$$\frac{63}{65}$$

Answer

$$-\frac{33}{65}$$

Answer

$$\frac{33}{65}$$

Answer

$$-\frac{63}{65}$$

Question 24

$$\sin96^o\cos24^o+\cos96^o\sin24^o\ $$ is equivalent to

Accepted Answer

$$\sin120^o$$

Answer

$$\sin72^{o\ }$$

Answer

$$\cos120^o$$

Answer

$$\cos72^o$$

Question 25

The expression $$2\sin30^o\cos30^o$$ has the same value as

Accepted Answer

$$\sin60^o$$

Answer

$$\sin15^o$$

Answer

$$\cos60^o$$

Answer

$$\cos15^o$$

Question 26

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

Accepted Answer

$$\cos\left( heta ight)$$

Answer

$$\sec\left( heta ight)$$

Answer

$$\sin\left( heta ight)$$

Answer

$$\csc\left( heta ight)$$

Question 27

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

Accepted Answer

$$ an^{2\ }\left( heta ight)$$

Answer

$$\cot^{2\ }\left( heta ight)$$

Answer

$$-\cot^{2\ }\left( heta ight)$$

Answer

$$- an^{2\ }\left( heta ight)$$

Question 28

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

Accepted Answer

$$\csc\left( heta ight)$$

Answer

$$\sin\left( heta ight)$$

Answer

$$\sec\left( heta ight)$$

Answer

$$ an\left( heta ight)$$

Trig Identities

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