Quiz about Trigonometric Identities Challenge

Question 1

*

Accepted Answer

csc2 x

Answer

sec2 x

Answer

cot2 x

Answer

tan2 x

Question 2

Question 2.

Accepted Answer

sec x

Answer

csc x

Answer

1/sec x

Answer

cos x

Question 3

Which of the following is NOT an Identity under Reciprocal Identity?

Accepted Answer

$$ an heta\ =\ \frac{\sin heta}{\cos heta}$$

Answer

$$\csc heta\ =\ \frac{1}{\sin heta}$$

Answer

$$\sec heta\ =\ \frac{1}{\cos heta}$$

Answer

$$1\ =\ \cot heta an heta$$

Question 4

$$Simplify\ \frac{1\ +\ an^2 heta}{\csc^2 heta}$$

Accepted Answer

$$ an^2 heta$$

Answer

$$\cos^2 heta$$

Answer

$$\sin^2 heta$$

Answer

$$1$$

Question 5

$$Simplify\ \frac{\sin^2x}{\sec^2-1}$$

Accepted Answer

$$\cos^2x$$

Answer

$$\sin^2x$$

Answer

0

Answer

1

Question 6

Which of the following should be written in Item number 1.

Accepted Answer

$$\frac{\cos x}{\cos x}$$

Answer

1

Answer

$$\frac{\sin x}{\sin x}$$

Answer

$$\frac{\cos x}{\sin x}$$

Question 7

Which of the following should be written in Item number 2.

Accepted Answer

1- cos x

Answer

cos x - 1

Answer

sinx - cos x

Answer

1 - sin x

Question 8

Which of the following should be written in Item number 3.

Accepted Answer

$$1\ -\ \cos^2x$$

Answer

1 - cosx

Answer

$$\frac{\cos x}{\cos x}$$

Answer

1

Question 9

Which of the following should be written in Item number 4.

Accepted Answer

$$1\ +\ \cos x$$

Answer

$$1-\cos x$$

Answer

$$1\ -\ \cos^2x$$

Answer

$$1\ +\ \cos^2x$$

Question 10

Which of the following should be written in Item number 1.

Accepted Answer

$$\sin^2x\ +\ \cos^2x$$

Answer

1

Answer

$$\sin x\ +\ \cos x$$

Answer

$$\sin^2x\ -\ \cos^2x$$

Question 11

Which of the following should be written in Item number 2.

Accepted Answer

$$\frac{1}{\cos^2x}$$

Answer

$$\cos^2x$$

Answer

$$\frac{1}{\cos x}$$

Answer

$$\csc^2x$$

Question 12

Which of the following should be written in Item number 3.

Accepted Answer

$$\csc^2x$$

Answer

$$\csc x$$

Answer

$$\frac{1}{\cos^2x}$$

Answer

$$\sin^2x$$

Question 13

What happens when you multiply two reciprocal functions?

Accepted Answer

It equals 1

Answer

You get a pythagorean identity

Answer

You get a quotient identity

Answer

It equals 0

Question 14

$$ an heta\cos heta$$ can be written in a single trigonometric identity as:

Accepted Answer

$$\sin heta$$

Answer

$$\cos heta$$

Answer

$$\sec heta$$

Answer

$$\cot heta$$

Question 15

$$\frac{1-\cos^2 heta}{\cos^2 heta}$$ can be written in a single trigonometric identity as:

Accepted Answer

$$ an^2 heta$$

Answer

$$\cos^2 heta$$

Answer

$$\sin^2 heta$$

Answer

$$\sec^2 heta$$

Question 16

$$\cos heta\ \csc heta$$ can be written in a single trigonometric identity as:

Accepted Answer

$$\cot heta$$

Answer

$$\cos heta$$

Answer

$$\sin heta$$

Answer

$$\sec heta$$

Question 17

Simplify

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

Accepted Answer

$$\cos^2 heta$$

Answer

$$\sec heta$$

Answer

$$\sin^2 heta$$

Answer

$$\frac{\sin^2 heta}{\cos^2 heta}$$

Question 18

Simplify

$$ an x\csc x\cos x$$

Accepted Answer

1

Answer

$$\frac{1}{\cos x}$$

Answer

$$\cot x$$

Answer

-1

Question 19

$$\frac{1-\cos^2 heta}{ an^2 heta}$$ can be simplified as

Accepted Answer

$$\cos^2 heta$$

Answer

$$\cot^2 heta$$

Answer

$$ an^2 heta$$

Answer

$$\sin^2 heta$$

Question 20

Which of the following would be a step to prove the following identity? $$\csc x-\sec x=\frac{\cos x-\sin x}{\sin x\cos x}$$

Accepted Answer

$$\frac{1}{\sin x}-\frac{1}{\cos x}$$

Answer

$$\frac{\cos x-\sin x}{\sin x}$$

Answer

$$\frac{\cos x-\sin x}{\cos x}$$

Answer

$$\frac{1}{\sin x\cos x}$$

Question 21

One step in proving the identity below would be:

$$\frac{\sec^2 heta-1}{\sec^2 heta}$$

Accepted Answer

Both A and B

Answer

$$\frac{\sec^2 heta}{\sec^2 heta}-\frac{1}{\sec^2 heta}$$

Answer

$$\frac{ an^2 heta}{\sec^2 heta}$$

Answer

Neither A nor B

Question 22

$$\frac{ an heta+\cot heta}{ an heta}$$ can be simplified as:

Accepted Answer

$$\csc^2 heta$$

Answer

$$\cot^2 heta$$

Answer

$$\sin^2 heta$$

Answer

$$\cos^2 heta$$

Question 23

$$\sin heta\cot heta\ \sec heta$$

Accepted Answer

$$1$$

Answer

$$0$$

Answer

$$\sin heta$$

Answer

$$\cos heta$$

Question 24

Simplify

$$\csc\ x\left(\cos x+\sin x\right)$$

Accepted Answer

cot x + 1

Answer

csc x

Answer

tan x + 1

Answer

cot x

Question 25

Simplify.

Accepted Answer

cos x

Answer

sin x

Answer

tan x

Answer

1

Question 26

5) tanxcotx-cos²x

Accepted Answer

sin2x

Answer

tanx

Answer

cotx

Answer

cos2x

Question 27

Simplify: $$\frac{\sin^2x+\cos^2x+\cot^2x}{1+ an^2x}$$

Accepted Answer

$$\cot^2x$$

Answer

$$	an^2x$$

Answer

$$\csc^2x$$

Answer

$$\sec^2x$$

Question 28

Simplify the trig expression.

Accepted Answer

2sinx

Answer

sinx

Answer

-sinx

Answer

cosx

Question 29

Simplify: $$\frac{\cos^2\left(-x\right)\csc x}{\cot x}$$

Accepted Answer

$$\cos x$$

Answer

$$-\sin x$$

Answer

$$-\cos x$$

Answer

$$\sin x$$

Question 30

Given the Csc(x) = 1, then the Sin(x) = ?

Accepted Answer

1

Answer

-1

Answer

0

Answer

Undefined

Question 31

Given the Cos(x) = -2/3, then the Sec(x) = ?

Accepted Answer

-3/2

Answer

-2/3

Answer

3/2

Answer

2/3

Question 32

Which of these is true because of even symmetry?

Accepted Answer

$$\cos\left(-40\degree\right)=\cos\left(40\degree\right)$$

Answer

$$\sin\left(-56\degree\right)=-\sin\left(56\degree\right)$$

Answer

$$ an\left(44\degree ight)=\cot\left(46\degree ight)$$

Answer

$$ an\left(12\degree ight)=\frac{1}{\cot\left(78\degree ight)}$$

Question 33

$$\cos\left(-\frac{4\pi}{5}\right)=$$
Complete this equation using even symmetry.

Accepted Answer

$$\cos\left(\frac{4\pi}{5}\right)$$

Answer

$$\frac{1}{\sec\left(-\frac{4\pi}{5}\right)}$$

Answer

$$\sin\left(-\frac{4\pi}{5}\right)$$

Answer

$$-\cos\left(\frac{4\pi}{5}\right)$$

Trigonometric Identities Challenge

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