AP Precalculus Review

AP Precalculus flashcards, Unit 3 Multiple Choice Questions.

Sine Equation for Wind Speed Experiment

A sine equation that describes the wave is V = 24 sin((π/16)(t-8)) + 40

Equation of the Graph

The equation that represents the graph is y = 3 sin(2x).

Phase Shift

The phase shift for the function f(x) = 2 sin(x - π/4) + 3 is π/4 units to the right.

Simplify the Identity

The simplified identity of sin²(x) + sin²(x)cot²(x) is 1.

Simplify the Expression

The simplified expression of (cos(x) / (1+sin(x))) + tan(x) is sec(x).

Exact Value

The exact value of the expression 2 sin(3π/4) + 3 tan(3π/4) is √2 - 3.

Period and Amplitude of Current

Period: 2/75 seconds; Amplitude: 120

Graph Transformation

The correct graph is NO

Value of sin θ

If cos θ = 4/9 and tan θ < 0, then sin θ = -√65 / 9.

Amplitude, Period, and Phase Shift

Amplitude: 2, Period: 2π/3, Phase Shift: π/3 right

Find tan θ

If sin θ = 5/6 and cos θ = -√11 / 6, then tan θ = -5√11 / 11

Exact Value of Expression

The exact value of cos[sin⁻¹(24/25)] is 7/25.

Secant Undefined

sec(x) is undefined for x = -3π/2, -π/2, π/2, 3π/2 where -2π ≤ x ≤ 2π

Transformation NOT Performed

Horizontal dilation by a factor of 2

Vertical Asymptotes of Cotangent

y = cot(x) has vertical asymptotes at -2π, -π, 0, π, 2π on the interval [-2π, 2π].

Simplified Form of cos²(x)-sin²(x)cos²(x)

cos⁴(x)

Find all solutions on [0,2π): 2 cos(x) - √3 = 0

The solutions are π/6 and 11π/6.

Inverse of f(x) = 9 sin(x) - 3

f⁻¹(x) = sin⁻¹((x+3)/9)

sin⁻¹(-0.5)

-π/6

sin(π/12)

(√6 - √2)/4

cos(11π/12)

(-√6 - √2)/4

Solve sin(2x)+sin(x)=0

0, π, 4π/3, 2π/3

Solve sin²(x) - cos²(x) = 0 on the interval [0, 2π)

π/4 , 3π/4, 5π/4, 7π/4

Value of periodic function at x = 20

-1

Point represented by (-4, 5π/6)

R

Alternate representation of (4, π/6) with r < 0, 0 < θ < 2π

(-4, -5π/6)

Rectangular coordinates of (7, 3π/4)

(-7√2 / 2, 7√2 / 2)

Convert the rectangular coordinates (4√3, 4) to polar coordinates.

(8, π/6)

Equation of polar graph

r = 4 cos(4θ)

Find all solutions in the interval [0, 2π), csc(x) + 2 = 0

7π/6, 11π/6

Maximum distance from the pole

5

Distance between f(θ) and the origin

I and II only

Values of a and d

a = 2 and d = 3

Sinusoidal regression

f(x) = 22.508 sin(0.465x - 1.576) + 40.654

Frequency

14.684

Graph of f(x)

For -π < x < 0, the graph of ƒ is decreasing at a decreasing rate.

Value of f(β)

0.368

Periodic function

g(x) = g(x+8)

Zeros of g on the interval 0 ≤ x ≤ π

1.042 and 2.130

Statements is true about the model for the elk population

The elk population is decreasing at an increasing rate on the interval 2.955 < t < 4.955.