# Lesson 15

Features of Trigonometric Graphs (Part 1)

### Problem 1

Here is a graph of a trigonometric function. Which equation could define this function?

A:

$$y = 1.5\sin(x) - 4$$

B:

$$y = 1.5\cos(x) - 4$$

C:

$$y = \text-4\sin(1.5x)$$

D:

$$y = \text-4\cos(1.5x)$$

### Problem 2

Select all the functions that have period $$\pi$$.

A:

$$y = \cos\left(\frac{x}{2}\right)$$

B:

$$y = \sin\left(\frac{x}{2}\right)$$

C:

$$y = \cos(x)$$

D:

$$y = \cos(2x)$$

E:

$$y = \sin(2x)$$

### Problem 3

1. Sketch a graph of $$a(\theta) = \cos(3\theta)$$.

2. Compare the graph of $$a$$ to the graph of $$b(\theta)=\cos(\theta)$$. How are the two graphs alike? How are they different?

### Problem 4

The functions $$f$$ and $$g$$ are given by $$f(x) = \cos(x)$$ and $$g(x) = \cos(5x)$$. How are the graphs of $$f$$ and $$g$$ related?

### Problem 5

Here is a point at the tip of a windmill blade. The center of the windmill is 6 feet off the ground and the blades are 1.5 feet long.

Write an equation giving the height $$h$$ of the point $$P$$ after the windmill blade rotates by an angle of $$a$$. Point $$P$$ is currently rotated $$\frac{\pi}{4}$$ radians from the point directly to the right of the center of the windmill.

### Solution

(From Unit 6, Lesson 14.)

### Problem 6

The coordinates of $$P$$ are $$(1,0)$$.

1. If the wheel makes a $$\frac{1}{3}$$ rotation counterclockwise around its center, what radian angle does $$P$$ rotate through?
2. If the wheel makes a $$1 \frac{1}{4}$$ rotation counterclockwise around its center, what radian angle does $$P$$ rotate through?

### Solution

(From Unit 6, Lesson 3.)

### Problem 7

A Ferris wheel has a radius of 95 feet and its center is 105 feet above the ground. Which statement is true about a point on the Ferris wheel as it goes around in a circle?

A:

It is 85 feet off the ground once in quadrant 1 and once in quadrant 2.

B:

It is is 85 feet off the ground once in quadrant 2 and once in quadrant 3.

C:

It is 85 feet off the ground once in quadrant 3 and once in quadrant 4.

D:

It is 85 feet off the ground once in quadrant 4 and once in quadrant 1.