Problem preview
F-TF.5 Warmup M3-036-A10-V01

Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.

Find when a sinusoidal model reaches its first maximum or minimum

Problem

For \(y=4\cos((\pi/6)(t-2))+10\), when does the first maximum at or after \(t=0\) occur?

Big Picture

What this problem is really about

First determine which trig-factor value produces the requested extreme, taking the outside coefficient's sign into account. Set the model's entire phase equal to every angle where that factor value occurs and solve for the repeating family of times. Finally, keep the earliest time in the allowed interval and substitute it back to verify the extreme output.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-TF.5
Category
Functions
Domain
Trigonometric Functions
Objective
Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Problem type
Find when a sinusoidal model reaches its first maximum or minimum