Precalculus: Trigonometric Identities and Equations flashcards

Question 1

What does sin²θ + cos²θ equal?

Accepted Answer

1

Question 2

What does 1 + tan²θ equal?

Accepted Answer

sec²θ

Question 3

What does 1 + cot²θ equal?

Accepted Answer

csc²θ

Question 4

What is sin(−θ) in terms of sin θ?

Accepted Answer

−sin θ

Question 5

What is cos(−θ) in terms of cos θ?

Accepted Answer

cos θ

Question 6

What is tan(−θ) in terms of tan θ?

Accepted Answer

−tan θ

Question 7

In an even-odd identity, what equation makes the identity odd?

Accepted Answer

f(−x) = −f(x)

Question 8

Which quotient identity gives tan θ?

Accepted Answer

tan θ = sin θ / cos θ

Question 9

Which quotient identity gives cot θ?

Accepted Answer

cot θ = cos θ / sin θ

Question 10

Which reciprocal identity gives csc θ?

Accepted Answer

csc θ = 1 / sin θ

Question 11

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

Accepted Answer

cos α cos β − sin α sin β

Question 12

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

Accepted Answer

cos α cos β + sin α sin β

Question 13

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

Accepted Answer

sin α cos β + cos α sin β

Question 14

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

Accepted Answer

sin α cos β − cos α sin β

Question 15

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

Accepted Answer

(tan α + tan β) / (1 − tan α tan β)

Question 16

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

Accepted Answer

(tan α − tan β) / (1 + tan α tan β)

Question 17

By a cofunction identity, sin θ equals the cosine of what angle?

Accepted Answer

π/2 − θ, so sin θ = cos(π/2 − θ)

Question 18

Double-angle formulas come from the sum formulas when what is true of the two angles?

Accepted Answer

The two angles are equal

Question 19

What is the double-angle formula for sin(2θ)?

Accepted Answer

sin(2θ) = 2 sin θ cos θ

Question 20

Write cos(2θ) using only the sine of θ.

Accepted Answer

cos(2θ) = 1 − 2 sin²θ

Question 21

Write cos(2θ) using only the cosine of θ.

Accepted Answer

cos(2θ) = 2 cos²θ − 1

Question 22

What is the double-angle formula for tan(2θ)?

Accepted Answer

tan(2θ) = 2 tan θ / (1 − tan²θ)

Question 23

What is the power-reducing formula for sin²θ?

Accepted Answer

sin²θ = (1 − cos 2θ) / 2

Question 24

What is the power-reducing formula for cos²θ?

Accepted Answer

cos²θ = (1 + cos 2θ) / 2

Question 25

What is the half-angle formula for sin(α/2)?

Accepted Answer

sin(α/2) = ±√((1 − cos α) / 2)

Question 26

What is the half-angle formula for cos(α/2)?

Accepted Answer

cos(α/2) = ±√((1 + cos α) / 2)

Question 27

Write the product cos α cos β as a sum.

Accepted Answer

½[cos(α − β) + cos(α + β)]

Question 28

Write the product sin α sin β as a difference.

Accepted Answer

½[cos(α − β) − cos(α + β)]

Question 29

Write sin α + sin β as a product.

Accepted Answer

2 sin((α + β)/2) cos((α − β)/2)

Question 30

Write cos α + cos β as a product.

Accepted Answer

2 cos((α + β)/2) cos((α − β)/2)

Precalculus: Trigonometric Identities and Equations flashcards

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