Q: Which of the following is the correct sum formula for the tangent function?

$$\tan(a+b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}$$

Q: Which of the following identities is correct for $$\tan(a-b)$$?

$$\tan(a-b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$$

Question 1

Which of the following is the correct sum formula for the sine function?

Accepted Answer

$$\sin(a+b) = \sin a \cos b + \cos a \sin b$$

Question 2

Given $$\sin a = \frac{3}{5}$$ with $$\frac{\pi}{2} \u003c a \u003c \pi$$ and $$\sin \beta = \frac{5}{13}$$ with $$0 \u003c \beta \u003c \frac{\pi}{2}$$, what is $$\cos(a+\beta)$$?

Accepted Answer

$$-\frac{56}{65}$$

Question 3

Which of the following is the correct difference formula for the cosine function?

Accepted Answer

$$\cos(a-b) = \cos a \cos b + \sin a \sin b$$

Question 4

If $$\sin 75^\circ = \sin(45^\circ + 30^\circ)$$, what is the exact value of $$\sin 75^\circ$$?

Accepted Answer

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

Question 5

Which of the following is the correct sum formula for the tangent function?

Accepted Answer

$$	an(a+b) = \frac{	an a + 	an b}{1 - 	an a 	an b}$$

Question 6

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

Accepted Answer

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

Question 7

Given $$\sin a = \frac{3}{5}$$ and $$\sin \beta = \frac{5}{13}$$, both in their respective quadrants, what is $$\sin(a+\beta)$$?

Accepted Answer

$$-\frac{16}{65}$$

Question 8

Which of the following identities is correct for $$	an(a-b)$$?

Accepted Answer

$$	an(a-b) = \frac{	an a - 	an b}{1 + 	an a 	an b}$$

Question 9

If $$\sin(\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta$$, what is $$\sin(\alpha + \beta)$$?

Accepted Answer

$$\sin \alpha \cos \beta + \cos \alpha \sin \beta$$

Question 10

A pilot is flying at an angle of elevation of $$30^\circ$$ and then changes to $$45^\circ. $$What is $$\sin(45^\circ - 30^\circ)$$?

Accepted Answer

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

Question 11

If $$	an a = 2$$ and $$	an b = 3$$, what is $$	an(a+b)$$?

Accepted Answer

$$-1$$

Question 12

Which of the following is a valid application of the sum formula for cosine?

Accepted Answer

$$\cos(a+b) = \cos a \cos b - \sin a \sin b$$

Question 13

If $$\sin 	heta = \frac{5}{13}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{12}{13}$$

Question 14

Given $$\sin a = \frac{3}{5}$$ and $$\cos a = -\frac{4}{5}$$, what is $$	an a$$?

Accepted Answer

$$-\frac{3}{4}$$

Question 15

If $$\sin(\alpha + \beta) = -\frac{16}{65}$$ and $$\cos(\alpha + \beta) = -\frac{56}{65}$$, what is $$	an(\alpha + \beta)$$?

Accepted Answer

$$\frac{4}{14}$$

Question 16

Which of the following is the correct formula for $$\cos(\alpha - \beta)$$?

Accepted Answer

$$\cos \alpha \cos \beta + \sin \alpha \sin \beta$$

Sum and Difference Formulas for Sine, Cosine, and Tangent Functions

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