Quiz about Trigonometric Identities Gp. Ac. 6

Question 1

$$\sin^2x+\cos^2x\ $$ is equal to

Accepted Answer

1

Answer

1-1

Answer

$$\sin^2x$$

Answer

$$\cos^2x$$

Question 2

The simpification of $$\frac{\sin^2x}{\cos^2x}$$ is

Accepted Answer

$$	an^2x$$

Answer

2cotx

Answer

2tan x

Answer

$$\cot^2x$$

Question 3

$$\cos^2x\ $$ is equal to

Accepted Answer

$$1-\sin^2x$$

Answer

$$1+\sin^2x$$

Answer

$$\sin^2x-a$$

Answer

$$\sin^2x$$

Question 4

The reciprocal of the cosecant

Accepted Answer

sine

Answer

tangent

Answer

cosine

Answer

secant

Question 5

The simplest form of $$\sin x\cos x\csc x$$

Accepted Answer

cosx

Answer

sinx

Answer

cscx

Answer

secx

Question 6

The simplest for of $$\sec^2x- an^2x$$ is

Accepted Answer

1

Answer

-1

Answer

senx

Answer

cosx

Question 7

Which identity would you use to simplfy the following expression, $$\cos x+\cot x\sin x$$

Accepted Answer

quotient

Answer

pythagorean

Answer

reciprocal

Answer

algebra

Question 8

Which rule was used in step 4 to get to step 5 of the proof

Accepted Answer

algebra

Answer

quotient

Answer

reciprocal

Answer

pythagorean

Question 9

Which rule was used in step 2 to complete the proof

Accepted Answer

pythagorean

Answer

reciprocal

Answer

algebra

Answer

quotient

Question 10

Which rule was used in step 2 to complete the proof

Accepted Answer

algebra

Answer

pythagorean

Answer

quotient

Answer

reciprocal

Question 11

Which rule was used in step 3 to complete the proof

Accepted Answer

algebra

Answer

pythagorean

Answer

reciprocal

Answer

quotient

Question 12

Which expression is not equal to 1

Accepted Answer

$$\csc^2x+\cot^2x$$

Answer

$$\sin^2x+\cot^2x\sin^2x$$

Answer

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

Answer

none of the above

Question 13

The simplest form of the following expression is $$\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}$$

Accepted Answer

2cscx

Answer

$$\frac{1}{2\sin x}$$

Answer

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

Answer

cscx

Question 14

The simplest form of the following expression is $$\csc x-\frac{\sin x}{1+\cos x}$$

Accepted Answer

cotx

Answer

tanx

Answer

$$\frac{\cos x+\cos^2x}{\sin x\ \left(1+\cos x\right)}^{ }$$

Answer

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

Question 15

The simplest form of the following expression is $$\left(1-\cos^2x\right)\left(1-\csc^2x\right)$$

Accepted Answer

$$-\cos^2x$$

Answer

$$\cos^2x$$

Answer

cosx

Answer

-cosx

Question 16

Find the solution of the equation in tne interval $$\lceil o,2\pi ceil$$

$$\cot heta=-2$$

Accepted Answer

$$ heta=2.68,5.82$$

Answer

$$ heta=0.468,\ 2.68$$

Answer

$$ heta=3.61,\ 5.82$$

Answer

$$ heta=2.68,3.61$$

Question 17

Find the solution of the equation in tne interval $$\lceil0,2\pi ceil$$

$$\sec heta=\frac{5}{4}$$

Accepted Answer

$$ heta=0.64,5.64$$

Answer

$$ heta=0.64,3.79$$

Answer

$$ heta=3.79,5.64$$

Answer

$$ heta=2.49,0.64$$

Question 18

Find the solutions of the equation in the interval $$\lceil0,2\pi ceil$$

$$\cos heta=\frac{4}{7}$$

Accepted Answer

$$ heta=0.96,5.32$$

Answer

$$ heta=0.96,4.10$$

Answer

$$ heta=2.17,5.32$$

Answer

$$ heta=4.10,5.32$$

Question 19

Find the solutions of the equations in the interval $$\lceil o,2\pi ceil$$

$$8\sin heta-4\sqrt[]{3}=0$$

Accepted Answer

$$ heta=\frac{\pi}{3},\frac{2\pi}{3}$$

Answer

$$ heta=\frac{\pi}{3},\frac{4\pi}{3}$$

Answer

$$ heta=\frac{4\pi}{3},\frac{5\pi}{3}$$

Answer

$$ heta=\frac{2\pi}{3},\frac{4\pi}{3}$$

Question 20

Find the solutions of the equation in the interval $$\lceil0,2\pi ceil$$

$$2\cos heta+1=0$$

Accepted Answer

$$ heta=\frac{2\pi}{3},\frac{4\pi}{3}$$

Answer

$$ heta=\frac{\pi}{3},\frac{4\pi}{3}$$

Answer

$$ heta=\frac{4\pi}{3},\frac{5\pi}{3}$$

Answer

$$ heta=\frac{\pi}{3},\frac{2\pi}{3}$$

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