Back to Exercise: Model periodic phenomena

Exercises: Choosing Trigonometric Functions to Model Periodic Phenomena

Show your work for each problem. Express answers involving pi using exact form (e.g., pi/4) unless otherwise stated.

Grade 9·24 problems·~30 min·Common Core Math - HS Functions·group·hsf-tf-b-5

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Warm-Up: Review What You Know

These problems review skills you have already learned.

In the function $y = \sin(x)$ , what is the period?

$\pi$

$2\pi$

$\frac{\pi}{2}$

$4\pi$

Which transformation moves the graph of $y = \sin(x)$ up 3 units?

$y = \sin(x + 3)$

$y = 3\sin(x)$

$y = \sin(3x)$

$y = \sin(x) + 3$

At $t = 0$ , a quantity is at its maximum value and then decreases. Which function best describes this starting behavior?

$y = \sin(t)$

$y = \cos(t)$

$y = -\sin(t)$

$y = \tan(t)$

Fluency Practice

Practice the core skills of this lesson.

What is the amplitude of $y = 4\sin(3x) - 2$ ?

$\frac{2\pi}{3}$

What is the period of $y = \cos\!\left(\frac{\pi}{6}x\right) + 1$ ?

Express your answer as a whole number.

What is the midline of $y = -5\cos(2x) + 7$ ?

Give the $y$ -value of the midline as a whole number.

A periodic phenomenon has a maximum value of 40 and a minimum value of 10. What is the amplitude?

$Parameter extraction table for a tidal height model: max 6 ft, min 0 ft, period 12.5 hr, midline 3 ft, amplitude 3 ft, B unknown$

A tide has a maximum height of 6 feet and a minimum height of 0 feet, completing one full cycle every 12.5 hours.

What is the value of $B$ in the sinusoidal model? Enter $B$ as a decimal rounded to three decimal places.

A pendulum displacement starts at its maximum positive value at $t = 0$ . The amplitude is 8 cm, the period is $\pi$ seconds, and the midline is $y = 0$ . Which equation models this?

$y = 8\sin(2t)$

$y = 8\cos(\pi t)$

$y = 8\cos(2t)$

$y = -8\cos(2t)$

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