AP Precalculus Unit 3 Flashcards

Flashcards for reviewing AP Precalculus Unit 3 topics.

Write a sine equation based on the wind speed experiment data.

Sine equation that describes the wave based on wind speed and time.

Find the equation of the given graph.

Equation representing a given graph.

Find the phase shift for the function f(x) = 2sin(x - *) + 3

*/4

Simplify the identity: sin^2(x) + sin^2(x)cot^2(x)

cos^2(x)

Simplify the expression: [sin(x) / (1 - cos(x))] + [tan(x)]

sec(x)

Find the exact value of the expression 2 sin^(-1)(*/2)

a

If I = 120sin(at), what are the period and amplitude of the current?

Amplitude: 120, Period: a

Sketch the graph of y = 2cos(x + */4) - 1

Graph of y = 2cos(x + */4) - 1

Find sin(8), if cos(8) = -3/5 and tan(8) < 0.

-4/5

Find the amplitude, period, and phase shift of y = 42sin[3(x - */6)]

Amplitude: 42, Period: */3, Phase Shift: */6

Find tan(8) if sin(8) = 4/5 and cos(8) = -3/5

-4/3

Find the exact value of the expression cos[sin^(-1)(7/25)]

-7/25

For what numbers x, 4/2 < x < 2, is sec(x) undefined?

x = 5*/2, x = */2

Which transformation was performed on y = sin(x) to obtain y = -3sin[2(x + */2)]?

Vertical stretch by a factor of 3, horizontal compression by a factor of 2, and horizontal translation */2 units to the left, reflection over the x-axis.

For what values of x does y = cot(x) have a vertical asymptote on the interval (2, 2]?

• , 2*

Factor and simplify: cos^4(x) - sin^2(x)cos^2(x)

cos^2(x)

Find all solutions on [0, 2*): 2cos(x) + sqrt(3) = 0

5/6, 7/6

Find the inverse of the function f(x) = 9sin(x) + 3

f^(-1)(x) = sin^(-1)((x - 3) / 9)

Find the exact value of the expression sin^(-1)(sqrt(3)/2)

*/3

Evaluate: sin(*/2)

Undefined

Evaluate: cos(*/2)

0

Find all solutions in the interval [0, 2*): sin(2x) + sin(x) = 0

0, 2*/3, *, 4*/3

Solve the equation on the interval [0, 2*): sin^2(x) - cos^2(x) = 0

/4, 3/4, 5/4, 7/4

Given a periodic function, what is the y-coordinate when x=20?

y-coordinate at x=20

Determine which point on the polar graph is represented by (-4, */5)

Polar coordinate representation

Find another representation of the polar coordinate (4, /2) with r < 0, 0 < 8 < 2

Another representation of the polar coordinate

For the polar coordinates (7, *), convert to rectangular coordinates

Rectangular coordinates

Given the rectangular coordinates (4sqrt(3), 4), convert to polar coordinates

Polar coordinates

Which equation represents the polar graph?

Polar graph equation

Find all solutions in the interval (0, 2*): csc(x) + 2 = 0

All solutions

What is the maximum distance from the pole in the polar graph?

Maximum distance from the pole

Given a polar function r = f(8), which statement is true about the distance from the origin?

Distance from the origin in polar function

What are the values of a and d for f(x) = acos[b(x + c)] + d, given min at (2,1) and max at (6,5)?

Values of a and d

Model the data using a sinusoidal regression.

Model data

Which gives the value of frequency of h(t) = 0.85sin(92.264t) + 1.25?

Frequency

Which of the following statements is correct about the graph of the function f?

Statement about the function's graph

If f(8) = tan(8), what is the value of f(8)?

Value of f(8)

Which could be true of g(x) for all x?

Function true for all x

What are the zeros of g on the interval 0 < x < 2?

Zeros of g

Which of the following statements is true about the model for the elk population?

True statement about the model for the elk population