Q: Which trigonometric identity is equivalent to $$\tan \theta = \frac{\sin \theta}{\cos \theta}$$?

$$\tan \theta = \frac{\sin \theta}{\cos \theta}$$

Q: Which of the following is a Pythagorean identity?

$$\sin^2$ \theta + \cos^2$ \theta = 1$$

Q: Which of the following is the correct reciprocal identity for $$\sec \theta$$?

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

Q: Which of the following is the correct factorization of $$\sin^2$ \theta + 6\cos \theta \sin \theta - 7\sin \theta$$?

$$\sin \theta (\cos \theta - 1)(\cos \theta + 7)$$

Q: Which of the following is the correct Pythagorean identity involving tangent and secant?

$$1 + \tan^2$ \theta = \sec^2$ \theta$$

Question 1

Which of the following is the correct factorization of $$3x^3$$ + $$42x^2$$?

Accepted Answer

$$6x^2(5x + 7$$)$$

Question 2

Given $$80\sin^4$ x - 30\sin x$$, what is the greatest common factor (GCF) you should factor out first?

Accepted Answer

$$10\sin x$$

Question 3

Which pair of numbers will correctly factor $$x^2 - 13x + 42$?

Accepted Answer

$$-6$$ and $$-7$$

Question 4

What is the correct factorization of $$6x^2 + 23x + 20$ using the grouping (AC) method?

Accepted Answer

$$(3x + 4)(2x + 5)$$

Question 5

Which trigonometric identity is equivalent to $$	an 	heta = \frac{\sin 	heta}{\cos 	heta}$$?

Accepted Answer

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

Question 6

Which of the following is a Pythagorean identity?

Accepted Answer

$$\sin^2$ 	heta + \cos^2$ 	heta = 1$$

Question 7

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 8

Which of the following is the correct factorization of $$2	an^2$ x + 9	an x - 35$$?

Accepted Answer

$$(2	an x - 5)(	an x + 7)$$

Question 9

Which of the following is the correct reciprocal identity for $$\sec 	heta$$?

Accepted Answer

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

Question 10

Which technique is most appropriate to simplify $$\frac{\sin 	heta}{1 + \cos 	heta}$$?

Accepted Answer

Multiply numerator and denominator by the conjugate $$1 - \cos 	heta$$

Question 11

Which of the following is the correct factorization of $$\sin^2$ 	heta + 6\cos 	heta \sin 	heta - 7\sin 	heta$$?

Accepted Answer

$$\sin 	heta (\cos 	heta - 1)(\cos 	heta + 7)$$

Question 12

Which of the following is the correct simplification for $$\sec 	heta 	an 	heta \csc 	heta$$?

Accepted Answer

$$\sec 	heta$$

Question 13

Which of the following is the correct simplification for $$\frac{1}{\sin x} + \frac{1}{\cos x}$$?

Accepted Answer

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

Question 14

Which of the following is the correct Pythagorean identity involving tangent and secant?

Accepted Answer

$$1 + 	an^2$ 	heta = \sec^2$ 	heta$$

Question 15

Which of the following is the correct simplification for $$\frac{\sin^2$ x + \cos^2$ x}{\sin x \cos x}$$?

Accepted Answer

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

Question 16

If $$	an 	heta = 3$$ and $$	heta is in $$the first quadrant, what is $$\sec^2$ 	heta$$?

Accepted Answer

$$10$$

Question 17

Which of the following is the correct simplification for $$\frac{1}{\sin x} + \frac{1}{\cos x}$$ after getting a common denominator?

Accepted Answer

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

Question 18

Which of the following is the correct simplification for $$\frac{\sin 	heta}{1 + \cos 	heta}$$ after multiplying numerator and denominator by $$1 - \cos 	heta$$?

Accepted Answer

$$1 - \cos 	heta$$

Question 19

Which of the following is the correct simplification for $$\frac{1}{\sin x} + \frac{1}{\cos x}$$ using reciprocal identities?

Accepted Answer

$$\csc x + \sec x$$

Factoring and Verifying Trigonometric Identities 5.1

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