AP Precalculus: Trigonometric Identities and Equations flashcards

Question 1

What is damped harmonic motion?

Accepted Answer

Oscillation like simple harmonic motion whose graph is changed by a damping factor, an energy-draining influence such as friction.

Question 2

From which formulas are the double-angle formulas derived?

Accepted Answer

From the sine, cosine and tangent sum formulas, taking both angles equal.

Question 3

Under the even-odd identities, when is f an odd function?

Accepted Answer

When f(-x) = -f(x).

Question 4

Under the even-odd identities, when is f an even function?

Accepted Answer

When f(-x) = f(x).

Question 5

From which formulas are the reduction formulas derived?

Accepted Answer

From the double-angle formulas.

Question 6

What do reduction formulas let you do to a trigonometric term?

Accepted Answer

Lower the power of the trigonometric function.

Question 7

What does a product-to-sum formula do?

Accepted Answer

Turns a product of trig functions into a sum or a difference of trig functions.

Question 8

What does a sum-to-product formula do?

Accepted Answer

Using substitution, turns a sum of trig functions into a product of trig functions.

Question 9

Which two ratios do the quotient identities express?

Accepted Answer

tan x = sin x / cos x and cot x = cos x / sin x.

Question 10

What do the reciprocal identities involve?

Accepted Answer

The reciprocals of the basic trigonometric functions.

Question 11

What is simple harmonic motion?

Accepted Answer

A repeating motion that can be modeled by a periodic sinusoidal oscillation.

Question 12

What is the sum formula for cos(a + b)?

Accepted Answer

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

Question 13

What is the difference formula for cos(a - b)?

Accepted Answer

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

Question 14

What is the sum formula for sin(a + b)?

Accepted Answer

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

Question 15

What is the difference formula for sin(a - b)?

Accepted Answer

sin(a - b) = sin a cos b - cos a sin b

Question 16

What is the sum formula for tan(a + b)?

Accepted Answer

tan(a + b) = (tan a + tan b) / (1 - tan a tan b)

Question 17

What is the difference formula for tan(a - b)?

Accepted Answer

tan(a - b) = (tan a - tan b) / (1 + tan a tan b)

Question 18

What kind of force does harmonic motion require?

Accepted Answer

A restoring force, such as gravity or a spring.

Question 19

In damped harmonic motion, what happens to the displacement when friction dissipates energy?

Accepted Answer

The displacement of the object shrinks.

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