Sum and Difference Identities flashcards

Question 1

What is the sum formula for cosine, cos(α + β)?

Accepted Answer

cos(α + β) = cos α cos β − sin α sin β

Question 2

What is the difference formula for cosine, cos(α − β)?

Accepted Answer

cos(α − β) = cos α cos β + sin α sin β

Question 3

What is the sum formula for sine, sin(α + β)?

Accepted Answer

sin(α + β) = sin α cos β + cos α sin β

Question 4

What is the difference formula for sine, sin(α − β)?

Accepted Answer

sin(α − β) = sin α cos β − cos α sin β

Question 5

What is the sum formula for tangent, tan(α + β)?

Accepted Answer

tan(α + β) = (tan α + tan β) / (1 − tan α tan β)

Question 6

What is the difference formula for tangent, tan(α − β)?

Accepted Answer

tan(α − β) = (tan α − tan β) / (1 + tan α tan β)

Question 7

In the cosine sum formula, what sign comes before the sin α sin β term?

Accepted Answer

A minus sign: cos(α + β) = cos α cos β − sin α sin β

Question 8

In the cosine difference formula, what sign comes before the sin α sin β term?

Accepted Answer

A plus sign: cos(α − β) = cos α cos β + sin α sin β

Question 9

Which two products appear in the sine sum formula?

Accepted Answer

sin α cos β and cos α sin β, added

Question 10

In the tangent sum formula, what is the denominator?

Accepted Answer

1 − tan α tan β

Question 11

In the tangent difference formula, what is the denominator?

Accepted Answer

1 + tan α tan β

Question 12

How is tan x written in terms of sine and cosine, and what condition does the section state?

Accepted Answer

tan x = sin x / cos x, with cos x ≠ 0

Question 13

How is the sum formula for tangent derived from the sine and cosine formulas?

Accepted Answer

Divide the sine sum formula by the cosine sum formula, then divide the numerator and denominator by cos α cos β

Question 14

What is the cofunction identity for sin θ?

Accepted Answer

sin θ = cos(π/2 − θ)

Question 15

What is the cofunction identity for cos θ?

Accepted Answer

cos θ = sin(π/2 − θ)

Question 16

What is the cofunction identity for tan θ?

Accepted Answer

tan θ = cot(π/2 − θ)

Question 17

What is the cofunction identity for cot θ?

Accepted Answer

cot θ = tan(π/2 − θ)

Question 18

What is the cofunction identity for sec θ?

Accepted Answer

sec θ = csc(π/2 − θ)

Question 19

What is the cofunction identity for csc θ?

Accepted Answer

csc θ = sec(π/2 − θ)

Question 20

Which three pairs of trigonometric functions are cofunctions of each other?

Accepted Answer

Sine and cosine, tangent and cotangent, secant and cosecant

Sum and Difference Identities flashcards

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Sum and Difference Identities flashcards

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