Lesson 1 George W. Ferris’ Day Off Develop Understanding

Ready

Find the other two trigonometric ratios based on the one that is given.

1.

$\sin θ = \frac{4}{5}$

a.

$\cos θ =$

b.

$\tan θ =$

2.

$\cos θ = \frac{5}{13}$

a.

$\sin θ =$

b.

$\tan θ =$

3.

$\tan θ = 1$

a.

$\sin θ =$

b.

$\cos θ =$

4.

$\sin θ = \frac{1}{2}$

a.

$\cos θ =$

b.

$\tan θ =$

5.

$\cos θ = \frac{9}{41}$

a.

$\sin θ =$

b.

$\tan θ =$

6.

$\tan θ = \sqrt{3}$

a.

$\sin θ =$

b.

$\cos θ =$

Set

Perhaps you have seen The London Eye in the background of a James Bond movie or on a television show. When it opened in March of 2000, it was the tallest Ferris wheel in the world. The passenger capsule at the very top is $135 meters$ above the ground. The diameter is $120 meters$ .

7.

How high is the center of the Ferris wheel?

8.

How far from the ground is the very bottom passenger capsule?

9.

Assume there are $36 passenger capsules$ , evenly spaced around the circumference. Find the height from the ground of each of the numbered passenger capsules shown in the figure. (Use the figure to help you think about the problem.)

a.

$1 =$

b.

$2 =$

c.

$3 =$

d.

$4 =$

e.

$5 =$

f.

$6 =$

g.

$7 =$

h.

$8 =$

Go

For problems 10 and 11, divide out all common factors.

10.

$\frac{16 - x^{2}}{6 x - 24}$

11.

$\frac{- 4 x - 8}{10 + 5 x}$

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

12.

$\frac{- 4 x + 8}{- 2 x - 10} \cdot \frac{x^{2} - 25}{6 - 3 x}$

13.

$\frac{9 x + 27}{2 x^{2} + 8 x + 8} \cdot \frac{4 x^{2} - 16}{6 x + 18}$

14.

$\frac{2 x^{2} + 7 x + 6}{2 x^{2} - 6 x - 20} \cdot \frac{15 - 3 x}{6 x + 6}$