The Cosine Function, Lesson 5, Unit 7

Find the period, range, and amplitude of the cosine function. y = 3/2 cos t/2 A) period = 4π, range: -3/2 ≤ y ≤ 3/2; amplitude = 3/2 B) period = 1/2, range: -3/2 ≤ y ≤ 3/2; amplitude = -3/2 C) period = 4π, range: -3/2 ≤ y ≤ 3/2; amplitude = -3/2 D) period = 1/2, range: y ≤ 3/2; amplitude = 3/2

A.

The motion of a simple spring hanging from the ceiling can be modeled with a cosine function. The bottom of the spring has a maximum height of 7 feet 4 inches and a minimum height of 6 feet 2 inches from the floor. It takes 2 seconds for the spring to expand from its minimum length to its maximum length. What is a cosine function that models the spring's length in inches above and below its average, resting position? Express the model as a function of time in seconds. A) f(t) = 7 cos ((π/2)t) B) f(t) = 14 cos ((π/2)t) C) f(t) = 7 cos (2πt) D) f(t) = 14 cos (2πt)

A.

What are all solutions to the equation 2 cos θ = 1 for 0 ≤ θ ≤ 2π? Round to the nearest hundredth. A) θ ≈ 1.32, 4.97 B) θ ≈ 1.05, 5.24 C) θ ≈ 0.52, 2.62 D) θ ≈ 0.05, 2.89

B.

What is the graph of one cycle of a cosine curve with amplitude 2, period 2π, and a < 0? A) https://imgur.com/bHmTVcP B) https://imgur.com/XNbty2o C) https://imgur.com/pNWUS6R D) https://imgur.com/b8NOezF

C.

Sketch one cycle of the cosine function. y = -cos 3θ A) https://imgur.com/ru4yrUs B) https://imgur.com/jUAhUxC C) https://imgur.com/Cg07UGc D) https://imgur.com/HUxq5Ka

D.