Question 1

Convert $$37.2^\circ to $$degrees, minutes, and seconds (DMS) format.

Accepted Answer

$$37^\circ 12'$$

Question 2

Convert $$42^\circ 6' 36'' to $$decimal degrees.

Accepted Answer

$$42.11^\circ$$

Question 3

A circle has a radius of $$3 cm. $$What is the length of the arc intercepted by a central angle of $$\frac{2\pi}{3}$$ radians?

Accepted Answer

$$2\pi cm$$

Question 4

In a South Carolina town, high tide occurs at 11:15 am at a depth of 18 inches, and low tide at 5:00 am at a depth of 6 inches. Which trigonometric equation best models the height $$y (in $$inches) of the water as a function of time $$t (in $$hours since midnight)?

Accepted Answer

$$y = 6 \cos\left(\frac{\pi}{6.25}(t-11.25)\right) + 12$$

Question 5

Based on your model for the tide, when does the next high tide occur after 11:15 am?

Accepted Answer

11:45 pm

Question 6

Steve is on a seesaw. At $$t=0$$ seconds, the distance from the top of his head to the ground is $$24$$ inches. At his highest point, it is $$60$$ inches. The seesaw completes a full cycle every $$3$$ seconds. What is the amplitude of the periodic function $$d(t)$$ modeling this motion?

Accepted Answer

$$18$$

Question 7

Given the function $$d(t) = 18 \sin\left(\frac{2\pi}{3}(t-3.75)\right) + 42$$, what is the midline of the graph?

Accepted Answer

$$y = 42$$

Question 8

For the function $$d(t) = 18 \sin\left(\frac{2\pi}{3}(t-3.75)\right) + 42$$, what is the period?

Accepted Answer

$$3$$ seconds

Question 9

Refer to the graph of $$d(t)$$ for Steve's seesaw. On the interval $$(t_1$, t_2$)$$, where $$t_1 is $$the $$t-$$coordinate of $$F$$ and $$t_2 is $$the $$t-$$coordinate of $$G$$, which statement is true?

Accepted Answer

$$d is $$positive and decreasing.

Question 10

On the interval $$(t_1$, t_2$)$$ between points $$F$$ and $$G on $$the graph of $$d(t)$$, how is the rate of change of $$d(t)$$ behaving?

Accepted Answer

The rate of change is decreasing because $$d(t) is $$concave down.

Question 11

If the arc length $$s of a $$circle is given by $$s = r	heta$$, where $$r is $$the radius and $$	heta is $$the central angle in radians, what is the arc length for $$r = 5 cm $$and $$	heta = \frac{\pi}{2}$$?

Accepted Answer

$$\frac{5\pi}{2} cm$$

Question 12

A periodic function modeling a real-world scenario has the form $$y = a \sin(b(t-c)) + d. $$Which parameter determines the vertical shift of the function?

Accepted Answer

$$d$$

Question 13

Suppose the depth of water at a dock varies sinusoidally with a minimum of $$4 ft at$$ $$2 am $$and a maximum of $$16 ft at$$ $$8 am. $$What is the midline of the function modeling this scenario?

Accepted Answer

$$y = 10$$

Question 14

If a function $$f(x)$$ has a period of $$T$$, which of the following is always true?

Accepted Answer

$$f(x) = f(x+T)$$

Question 15

A Ferris wheel has a radius of $$10$$ meters and rotates once every $$20$$ seconds. If a rider starts at the lowest point, which equation models the height $$h (in $$meters) above the ground as a function of time $$t (in $$seconds)?

Accepted Answer

$$h(t) = 10 \sin\left(\frac{\pi}{10} t - \frac{\pi}{2}\right) + 10$$

Precalculus Study Guide: Angles, Arc Length, and Trigonometric Modeling

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