Question bank: Trigonometric Function: Periodicity

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Question 1:

Easy

What is the period of the trigonometric function f(x) = 2 sin(3x)?

Trigonometric Function: Periodicity

Question 2:

Medium

Ana is a civil engineer who is designing an amusement park toy that goes up and down according to a trigonometric function. The toy goes up and down with a periodicity of 2 minutes. The movement of the toy can be described by the function h(t) = a sin(b(t-c)) + d, where 'a' is the amplitude, 'b' defines the period, 'c' is the horizontal phase, and 'd' is the vertical phase. Ana needs to design the toy so that it reaches a maximum height (amplitude) of 10 meters and is on the ground (vertical phase) when t = 0. Your question is: what is the function h(t) that describes the movement of the toy?

Trigonometric Function: Periodicity

Question 3:

Medium

A sound wave emitted by a musical instrument can be mathematically modeled by a trigonometric function. Consider the function f(x) = 3sin(2x + pi/3). Based on the expression of the given function, determine the period of the function and justify your answer using the properties of sine and cosine functions.

Trigonometric Function: Periodicity

Theorical Question

Contextualized Question

Question 4:

Medium

A ferris wheel has a radius of 10 meters and completes a full circular motion every 2 minutes. A seat of the ferris wheel is initially at a height of 12 meters above the ground. Consider the function that describes the height (in meters) of a seat as a function of time (in minutes), h(t) = 10sin(πt) + 12. Determine the period of this function and at what time t the seat will be at a height of 20 meters.

Trigonometric Function: Periodicity

Question 5:

Medium

What is the period of the trigonometric function f(x) = cos(3x)?

Trigonometric Function: Periodicity

IARA TIP

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