Lesson 2 “Sine” Language Solidify Understanding

Ready

For each graph, identify the domain and range. Then write the interval(s) where $f (x)$ is positive, $f (x) > 0$ , and the interval(s) where $f (x)$ is negative, $f (x) < 0$ .

1.

a.

Domain:

b.

Range:

c.

Positive:

d.

Negative:

2.

a.

Domain:

b.

Range:

c.

Positive:

d.

Negative:

3.

a.

Domain:

b.

Range:

c.

Positive:

d.

Negative:

4.

a.

Domain:

b.

Range:

c.

Positive:

d.

Negative:

Write the piecewise equation that describes each graph.

5.

6.

Set

Recall the following facts from the lesson done in class:

The Ferris wheel has a radius of $25 feet$ .
The center of the Ferris wheel is $30 feet$ above the ground.

Due to a safety concern, the management of the amusement park decides to slow the rotation of the Ferris wheel from $20 seconds$ for a full rotation to $30 seconds$ for a full rotation.

7.

Calculate how high a rider will now be $2 seconds$ after passing position $A$ on the diagram.

8.

a.

Calculate the height of a rider at each of the following times $t$ , where $t$ represents the number of seconds since the rider passed position $A$ on the diagram.

Elapsed time since passing position $A$	Calculations	Height of the rider (in feet)
$1 second$
$3 seconds$
$5 seconds$
$7 seconds$
$8 seconds$
$11 seconds$
$14 seconds$
$15 seconds$
$16 seconds$
$20 seconds$
$22 seconds$
$23 seconds$
$25 seconds$
$27 seconds$
$30 seconds$

b.

Plot the position you calculated on the diagram. Connect the center of the circle to the point you plotted. Then draw a vertical line from the plotted point on the Ferris wheel to the line segment $A F$ in the diagram. Each time you should get a right triangle similar to the one in the figure.

9.

How did the position of the triangles you drew change between $7 seconds$ and $8 seconds$ ?

10.

How did the triangles you drew change between $14$ , $15$ , and $16 seconds$ ?

11.

How did the triangles you drew change between $22 seconds$ and $23 seconds$ ?

12.

Describe a relationship between the angle $(θ)$ the hypotenuse makes with the $x$ -axis in each triangle and the angle of rotation. Use the diagram to help you think about the question. (The dotted arc shows the angle of rotation.)

Go

Perform the indicated operation. Divide out all common factors in your answers.

(Assume no denominator is equal to $0$ .)

13.

$\frac{7 x - 10}{3 x - 12} - \frac{x + 8}{3 x - 12}$

14.

$\frac{5 x^{2} - 8 x}{x^{2} - 9} - \frac{4 x + 9 x^{2}}{x^{2} - 9}$

15.

$\frac{3 x - 5}{2 x - 6} - \frac{4 x - 2}{5 x - 15}$

16.

$\frac{x - 10}{x - 4} - \frac{x + 2}{4 - c}$

17.

$\frac{2 x + 11}{x + 2} - \frac{2 x - 3}{- x - 2}$

18.

$\frac{3}{4 x - 12} - \frac{3}{3 - x}$