NAME , • - • EATE PERIOD)

2 Practice

Angles and Angle Measure O Draw an angle with the given measure in

standard position. - -

1, 21.0° 2, 305° 3, 580°

W J

7 3– , –560°

Rewrite each degree measure in radians and each radian measure in degrees.

As Find one angle with positive measure and one angle with negative measure

* & po -29 E } . (p4% – 15 23.65 L25, J)

3 7 3.

NAME DATE PERIOD

Practice Trigonometric Functions of General Angles O h

Find the exact values of the six trigonometric functions of 6 if the terminal side of 6 in

standard position contains the given point.

1, 6,8) 2. 20, 21) war- -2g -- - - . P _ (ry" - COC -- sur, Is ce: Sún 3: C2C 23

2 Coo Tae9 A2C-ad woo -aw 23

A& - a an3 coe 24 : coo -33 &

- ourn 3: Find the reference angle for the angle with the given

measure.

Find the exact value of each trigonometric function. AI2 2.

T212. tan ass- 3 13, cSc (-)- 2. 1: - 3 O - 3 O

Suppose 6 is an angle in standard position whose terminal side is in the given

quadrant. For each function, find the exact values of the remaining five

trigonometric functions of ,

NAME .

Practice

Circular Functions

Fhe given point P is located on the unit circle. Find sin 9 and cos 9. 1. P) .

P08, .6)

C O9 he lot

Find the exact value of each function.

2- 2- 2. - 2

Determine the period of each function. .

Graehi nd Trig

O eraer Sine outou-ng . - l . J =

Asun e - 1

- 2, 2 g

="sen a e - 3 4,

3 = + coe e + 2 5.

48 H I

Trig C) . 3 traplify

eo-c Yn expre ssion l. on

e - CSC G (1)

Gec G -

3 sec G e cot e G

( - sun e ( A sun e

A.

O

9 .

(o .

-7 .

ar e sun e Coa e >

cot e Gee O

Trig Application

In an amusement park, there is a small Ferris wheel, called a kiddle wheel, for toddlers.

We will use the points on the circle in the diagram at right to represent the position of

the cars on the wheel. The kiddle wheel has four cars, makes#

gr) nityrand

ground to a car at the lowest point is 5 feet. Assume t = 0 corresponds to a

time wheth car 1 is closest to the ground. -

32

in the classic novel, Don Quixote, the title character famously battles a windmill.

In this problem, you will model what happens when Don Quixote battles a

windmill, and the windmill wins. Suppose the center of the windmill ls 20 feet off

the ground, and the sails are 15 feet long, Don Quixote is caught on a tip of one of

the sails. The sails

The High Roller, a Ferrls wheel In Las Vegas, Nevada, opened in March 2014. The 550 ft, tail wheel

has a diameter of 520 feet, Aride an one of its 2B passenger cars lasts 30 minutes, the tline it

takes the wheel to complete one fulf rotation. Riders board the passenger cars at the bottom of

the wheel. Assume that once the wheel ls in motion,

- -. - It maintains a constant speed forthg80milittérldnd is rotating in a

counterclockwise direction.

OAs you ride the Ferris wheel, your distance from

the ground

varies sinusoidally with time. Lett be the number of

seconds that have elapsed since the Ferris Wheel started

(this does not include loading the Ferris wheel). You find

that it takes you 3 seconds to reach the top, 43 feet above

seconds, The diameter of the wheels 20

feet" , a = 32- 2C = 23 For the Fourth of July parade, Vicki decorated her tricycle with streamers and balloons.

She stuck one balloon on the outside rim of one of her back tires. The balloon starts at

ground level. As she rides, the height of balloon rises up and down, sinusoidally (that is,

a sine curve, The diameter of her tire is 10 inches.

ground, and that wheel makes a revolu

31, Sketch a graph showing the height of the balloon above the ground as

Vicki rolls along. _NsL------

W l of il HCoheel onalko- one rocellor ourio UUnd --) b. hat is the period of this graph" --

- O 2:cence 26-tect cle- C = 2-1Cr, C = 2 g" C, Write the equation of this function, – - 2

+

O = 5 b = 2: ol5- - 5 coo d. Use your equation to Mict the Hei ght of the balloon after

Vicki has traveled 42 inches.

3. 415

A wooden water wheel is next to an old stone mill. The water wheel

makesignergyolutiétist

afety-miniité dips down two feet below the surface of the water, and at

its highest point is E feet above the water, A snail attaches to the edge

of the wheel when the wheel is at its lowest point and rides the wheel

as it goes round and around. As time passes, the snail

rises up and down, and in fact, the height of the snail above the surface of

the water varies sinusoidally with time. Use this information to write the

particular equation that gives the

height of Snai t- - - W --7height of the snail over time O revo td. C Wo - 2n- " -23

Te -1 C2

1 CoO C222. . - l” S 2 T To keep baby Cristina entertained, her mother

often puts her in a Johnny Jump Up. It is a t) t- (9 (0 : on the end of a strong

spring which attaches in a doorway. When Mom puts Cristina , -2 - sfah,

she notices that the seat drops to just 8 inches above the floor. One and a

half seconds e 2-0

later (isis), the seat reaches its highest point of 20 inches above the ground. The

• e: continues to bounce up and down as time passes. Use this information to

write the - 4 &

5articular equation that gives the height of baby Cristinas Johnny Jump Up seat

over time, - Note: You can start the graph at the point where the seat is at its

lowest) • 3422–