Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round to two decimal places.

W ARM -U P E XERCISES Simplify.

1. ^{7 π}

3 − 2π 2. − 5 π

6 + 2π

Find the measure of the angle in degrees between the hour hand and the minute hand of a clock at the time shown. Measure the angle in the clockwise direction.

3. 12:30 4. 5:40

Find the area of the circle with the given radius.

5. r = 3 in. 6. r = 1.5 ft

D AILY H OMEWORK Q UIZ

Determine the quadrant in which each angle lies. Then convert the angle measure from radians to degrees. Round to two decimal places.

1. ^{2 π}

5 2. _−1.8π 3. ⁷

3

Find the length of the arc on a circle of radius r intercepted by a central angle θ.

Round to two decimal places.

4. r = 11 in.; θ = 100º 5. r = 3.6 ft; θ = 290º 6. r = 20 cm; θ = ^π 3

A NSWERS

WU 1. ^π

3 2. ^{7 π}

6 3. 165º 4. 70º

5. _9π in.

²

6. _2.25π ft

²

S ECTION 4.2

W ARM -U P E XERCISES

Rewrite each angle in degree measure. (Do not use a calculator.) 1. ^{3 π}

4 2. ^{10 π}

3 3. − 13 π

6 4. ^π

12 Classify each function as odd, even, or neither.

5. f(x) = 6x

³

+ 3x 6. g(x) = |x| 7. f(x) = 2x

²

– 8x

D AILY H OMEWORK Q UIZ

Evaluate (if possible) the six trigonometric functions of the real number.

1. t = 3 π

4 2.

t = − 11 π

6 3.

t = π 3

Use the value of the trigonometric function to evaluate the given functions.

4. sin t = 0.8 (a) sin (–t) (b) csc t 5. cos (–t) = − 3

5 (a) cos (! – t) (b) sec t

WU 1. 135º 2. 600º 3. –30° 4. 15º

5. odd 6. even 7. neither

QUIZ 1. sin 3 π 4

⎛

⎝⎜

⎞

⎠⎟ = 2

2 ; cos 3 π 4

⎛

⎝⎜

⎞

⎠⎟ = − 2

2 ; tan 3 π 4

⎛

⎝⎜

⎞

⎠⎟ = −1;

csc 3 π 4

⎛

⎝⎜

⎞

⎠⎟ = 2; sec 3 π 4

⎛

⎝⎜

⎞

⎠⎟ = − 2; cot 3 π 4

⎛

⎝⎜

⎞

⎠⎟ = −1 2. sin − 11 π

6

⎛

⎝⎜

⎞

⎠⎟ = 1

2 ; cos − 11 π 6

⎛

⎝⎜

⎞

⎠⎟ = 3

2 ; tan − 11 π 6

⎛

⎝⎜

⎞

⎠⎟ = 3 3 ;

csc − 11 π 6

⎛

⎝⎜

⎞

⎠⎟ = 2; sec − 11 π 6

⎛

⎝⎜

⎞

⎠⎟ = 2 3

3 ; cot − 11 π 6

⎛

⎝⎜

⎞

⎠⎟ = 3 3. sin π

3

⎛

⎝⎜

⎞

⎠⎟ = 3

2 ; cos π 3

⎛

⎝⎜

⎞

⎠⎟ = 1

2 ; tan π 3

⎛

⎝⎜

⎞

⎠⎟ = 3;

csc π 3

⎛

⎝⎜

⎞

⎠⎟ = 2 3

3 ; sec π 3

⎛

⎝⎜

⎞

⎠⎟ = 2; cot π 3

⎛

⎝⎜

⎞

⎠⎟ = 3 3 4. (a) –0.8 (b) 1.25

5. (a) ³

5 (b) − 5

3

S ECTION 4.3

W ARM -U P E XERCISES

The lengths of the legs of a right triangle are given. Find the length of the hypotenuse.

1. 3 cm, 5 cm 2. 2 in., 6 in.

Evaluate (if possible) the six trigonometric functions of the real number.

3. t = 5 π 4

4. t = − 3 π 2 5. t = π

6

D AILY H OMEWORK Q UIZ

1. Find the exact values of the six trigonometric functions of the angle θ for the triangle.

Use trigonometric identities to transform the left side of the equation into the right side (0 < θ < !/2).

2. _tan

²

α ^csc

²

α = sec

²

α

3. sinθ + cotθ cosθ = cscθ

WU 1. ₃₄ cm 2. _{2 10} in.

3. sin 5 π 4

⎛

⎝⎜

⎞

⎠⎟ = − 2

2 ; cos 5 π 4

⎛

⎝⎜

⎞

⎠⎟ = − 2

2 ; tan 5 π 4

⎛

⎝⎜

⎞

⎠⎟ = 1;

csc 5 π 4

⎛

⎝⎜

⎞

⎠⎟ = − 2; sec 5 π 4

⎛

⎝⎜

⎞

⎠⎟ = − 2; cot 5 π 4

⎛

⎝⎜

⎞

⎠⎟ = 1 4. sin − 3 π

2

⎛

⎝⎜

⎞

⎠⎟ = 1; cos − 3 π 2

⎛

⎝⎜

⎞

⎠⎟ = 0; csc − 3 π 2

⎛

⎝⎜

⎞

⎠⎟ = 1; cot − 3 π 2

⎛

⎝⎜

⎞

⎠⎟ = 0 5. sin π

6

⎛

⎝⎜

⎞

⎠⎟ = 1

2 ; cos π 6

⎛

⎝⎜

⎞

⎠⎟ = 3

2 ; tan π 6

⎛

⎝⎜

⎞

⎠⎟ = 3 3 ;

csc π 6

⎛

⎝⎜

⎞

⎠⎟ = 2; sec π 6

⎛

⎝⎜

⎞

⎠⎟ = 2 3

3 ; cot π 6

⎛

⎝⎜

⎞

⎠⎟ = 3 QUIZ 1. sin θ = 3

7 ; cos θ = 2 10

7 ; tan θ = 3 10 20 ;

csc θ = 7

3 ; sec θ = 7 10

20 ; cot θ = 2 10 3

2. tan

²

α csc

²

α = sin

²

α cos

²

α

⎛

⎝⎜

⎞

⎠⎟

1 sin

²

α

⎛

⎝⎜

⎞

⎠⎟ = 1

cos

²

α = sec

²

α 3. sin θ + cotθ cosθ = sinθ + cos θ

sin θ (cos θ) = sinθ + cos

²

θ sin θ = sin

²

θ

sin θ + cos

²

θ

sin θ = sin

²

θ + cos

²

θ

sin θ = 1

sin θ = cscθ

S ECTION 4.4

W ARM -U P E XERCISES

Determine the quadrant in which each angle lies.

1. 77º 2. 240º 3. –9º

Find the values of θ in degrees (0º < θ < 90º) and radians (0 < θ < !/2) without the aid of a calculator.

4. cos θ = 3

2 5. tan θ = 3

3 6. _{cscθ = 2}

D AILY H OMEWORK Q UIZ

Find the values of the six trigonometric functions of θ with the given constraint.

1. tan θ = 2; θ lies in Quadrant III.

2. sin θ = − 1

6 ; cos θ > 0

3. sec θ is undefined; ! < θ < 2!

Evaluate the sine, cosine, and tangent of the angle without using a calculator.

4. 240º

5. − 9 π

4

WU 1. Quadrant I 2. Quadrant III 3. Quadrant IV 4. 30º, ^π

6 5. 30º, ^π

6 6. 45º, ^π

4

QUIZ 1. sin θ = − 2 3

3 ; cos θ = − 3

3 ; tan θ = 2;

csc θ = − 3

2 ; sec θ = − 3; cotθ = 1 2

2. sin θ = − 1

6 ; cos θ = − 35

6 ; tan θ = − 35 35 ;

csc θ = −6; secθ = − 6 35

35 ; cot θ = − 35 3. sinθ = −1; cosθ = 0; cscθ = −1; cotθ = 0 4. sin 240 ° = − 3

2 ; cos 240 ° = − 1

2 ; tan 240 ° = 3 5. sin − 9 π

4

⎛

⎝⎜

⎞

⎠⎟ = − 2

2 ; cos − 9 π 4

⎛

⎝⎜

⎞

⎠⎟ = 2

2 ; tan − 9 π 4

⎛

⎝⎜

⎞

⎠⎟ = −1

S ECTION 4.5

W ARM -U P E XERCISES

Evaluate the trigonometric function of the quadrant angle.

1. cos π 2

⎛

⎝⎜

⎞

⎠⎟

2. sin 3 π 2

⎛

⎝⎜

⎞

⎠⎟

Find two solutions of the equation. Give your answers in radians (0 < θ < 2!).

3. cos( θ) = − 1 2

4. sin( θ) = 3 2 5. cos(θ) = 0

D AILY H OMEWORK Q UIZ Find the period and amplitude.

1. y = −3cosπx 2. y = 3

2 sin x 4

Sketch the graph of the function. (Include two full periods.) 3. y = −cos(x − π )

4.

y = 2

3 sin π ^x 3

⎛

⎝⎜

⎞

⎠⎟ + 2

WU 1. 0 2. –1 3. ^{2 π} 3 , 4 π

3 4. ^π

3 , 2 π

3 5. ^π

2 , 3 π 2

QUIZ 1. 3; 2 2. ³

2 ; π 2 3.

4.

5.

S ECTION 4.6

W ARM -U P E XERCISES

Sketch the graph of the function. (Include two full periods.) 1. y = −2sin(πx)

2. y = 2 + cos(x − π ) 3.

y = 1

2 sin x 2 − π

4

⎛

⎝⎜

⎞

⎠⎟

Find the period and the amplitude of the trigonometric function.

4.

y = 5cos π ^x 3

⎛

⎝⎜

⎞

⎠⎟

5. y = −sin(3x + π ) 6. y = 2

3 cos(x)

D AILY H OMEWORK Q UIZ

Sketch the graph of the function. (Include two full periods.) 1. y = 2tanπx − 1

2.

y = 1

2 sec x + π 2

⎛

⎝⎜

⎞

⎠⎟

3. y = −2 + cot(2πx)

Use a graph to solve the equation on the interval [–2!, 2!].

4. cot x = −1

2 3

WU 1. 2.

3.

4. 6; 5 5. ^{2 π}

3 ; 1 6. 2 π; 2 3

QUIZ 1. 2.

3.

4. − 5 π 4 , − π

4 , 3 π 4 , 7 π

4 5. − 11 π

6 , − π 6 , π

6 , 11 π 6

6. − 5 π 6 , − π

6 , 7 π 6 , 11 π

6

W ARM -U P E XERCISES

Use the properties of inverse functions to evaluate the expression.

1. f

^–1

(f(–2)) 2. f(f

^–1

(13))

Expressions representing the legs of a right triangle are given. Write an expression to represent the hypotenuse.

3. 5x; 3 4. (x – 2); x

Use a calculator to evaluate the expression. Round your result to two decimal places.

5. sin 1.9 6. csc (–2) 7. cot (11º)

D AILY H OMEWORK Q UIZ

Evaluate the expression without using a calculator.

1. arccos 1 2. tan

⁻¹

3

3

⎛

⎝ ⎜ ⎞

⎠ ⎟

Find the exact value of the expression. (Hint: Sketch a right triangle.) 3. tan arccos − 4

5

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣ ⎢

⎢

⎤

⎦ ⎥

⎥ 4. csc tan ⎡⎣

⁻¹

(3) ⎤⎦

Write an algebraic expression that is equivalent to the expression.

5. sin (arccos 2x) 6.

cot arcsin 2 x

⎛

⎝⎜

⎞

⎠⎟

A NSWERS

WU 1. –2 2. 13 3. _25x

²

+ 9 4. _2x

²

− 4x + 4

S ECTION 4.8

W ARM -U P E XERCISES

Use a calculator to evaluate the expression. Round your result to two decimal places.

1. arccos 0.73 2. arctan 3 3. sin

^–1

0.45 4. tan

^–1

(–1.5)

5. A child holds a balloon in her hand at a height of 3 feet. The balloon is attached to a 25-inch string, and the wind blows the balloon so the string forms an angle θ from vertical. Write θ as a function of the height h of the balloon, in inches.

D AILY H OMEWORK Q UIZ

1. The sun is 13º above the horizon. Find the height of a road sign that casts a shadow 18 feet long. Round your answer to two decimal places.

2. An airplane is 120 miles south and 45 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? Round your answer to two decimal places.

3. A piece of paper measures 8 inches by 10 inches. A corner is folded over so that it touches the long side at its midpoint. What is the angle formed by the corner and the long side? Round your answer to the nearest degree.

A NSWERS

WU 1. 0.75 2. 1.25 3. 0.47

4. –0.98 5.

θ = cos

⁻¹

h − 3 25

⎛

⎝⎜

⎞

⎠⎟