Test 1 Review

Determine quadrant: (a) -5π/12 (b) -13π/9

(a) Quadrant IV (b) Quadrant II

Find the angle difference in D°M'S'' form: 120°45'29'' and 12°36'3''

108°9'26''

Find reference angle: -165°

15°

Find the central angle θ: r=80 km. s=160 km.

2 rad

A voltmeter's pointer is 6 centimeters in length. Find the number of degrees through which it rotates when it moves 2.5 centimeters on the scale.

23.873224146°

Find the remaining trig functions. cosθ=-3/7 sinθ<0

sinθ=-2(√10)/7 tanθ=2(√10)/3 cscθ=-7(√10)/20 secθ=-7/3 cotθ=3(√10)/20

Convert to radians: (a) -330° (b) 144°

(a) -11π/6 (b) 4π/5

Convert to degrees: (a) -15π/6 (b) 28π/15

(a) -450° (b) 336°

Convert to degrees: (a) -4π (b) 3π

(a) -720° (b) 540°

Use a calculator to evaluate each function: (a) tan18.5° (b) cot71.5°

(a) 0.3345953195 (b) 0.3345953195

Use a calculator to evaluate each function: (a) cos8°50'25'' (b) sec56°10''

(a) 0.98812059131 (b) 1.78842019761

Determine two coterminal angles in radian measure (one positive and one negative): (a) 7π/6 (b) 5π/4

(a) 19π/6, -5π/6 (b) 13π/4, -3π/4

Determine two coterminal angles in degree measure (one positive and one negative): (a) -445° (b) 230°

(a) 275°, -85° (b) 590°, -130°

Use a calculator to evaluate each function: (a) sec1.54 (b) cos1.25

(a) 32.4765382934 (b) 0.31532236239

Determine two coterminal angles in degree measure (one positive and one negative): (a) 114° (b) -390°

(a) 474°, -246° (b) 330°, -30°

The number of revolutions made by a figure skater for each type of axel jump is given. Determine the measure of the angle generated as the skater performs each jump. Give the answer in both degrees and radians. (a) Single axel: 1.5 revolutions (b) Double axel: 2.5 revolutions. (c) Triple axel: 3.5 revolutions

(a) 540°, 3π (b) 900°, 5π (c) 1260°, 7π

Convert to radians: (a) 315° (b) 120°

(a) 7π/4 (b) 2π/3

The circular blade on a saw has a diameter of 7.25 inches and rotates at 4800 revolutions per minute. (a) Find the angular speed of the blade in radians per minute. (b) Find the linear speed of the saw teeth (in inches per minute) as they contact the wood being cut.

(a) 9600π rad/min (b) 109327.4243 in/min

Determine two coterminal angles in radian measure (one positive and one negative): (a) -7π/8 (b) π/12

(a) 9π/8, -23π/8 (b) 25π/12, -23π/12

Determine quadrant: (a) 87.9° (b) -8.5°

(a) Quadrant I (b) Quadrant IV

Determine quadrant: (a) -245.25° (b) 12.35°

(a) Quadrant II (b) Quadrant I

Determine quadrant: (a) 5π/6 (b) -5π/3

(a) Quadrant II (b) Quadrant I

Determine quadrant: (a) 121° (b) 181°

(a) Quadrant II (b) Quadrant III

Determine quadrant: (a) 3.5 (b) 2.25

(a) Quadrant III (b) Quadrant II

Convert to radians: -46.52°

-0.811927168

Convert to D°M'S'' form: -115.8°

-115°48'

Convert to decimal degree form: -124°30'

-124.5°

Convert to degrees: -0.57

-32.65859432°

Convert to decimal degree form: -408°16'25''

-408.2736111°

Find the angle difference in D°M'S'' form: 36°8'43'' and 81°17''

-44°51'34''

Convert to degrees: -4.2π

-756°

Find reference angle: -6.5

0.2168146928

Find the radius r: s=3 m. θ=4π/3

0.71619724391 m

Find the radius r: s=8 in. θ=330°

1.38898859426 in

Convert to radians: 83.7°

1.460840584

Find the reference angle: -330°

30°

Convert to decimal degree form: 330°25''

330.0069444°

Find reference angle: 322°

38°

Find the arc length s: r=9 ft. θ=π/3

3π ft

Find the reference angle: 225°

45°

Find the reference angle: 315°

45°

Convert to D°M'S'' form: 45.063°

45°3'47''

Convert to D°M'S'' form: 490.75°

490°45'

Find the central angle θ: r=22 ft. s=10 ft.

5/11 rad

Convert to radians: 395°

6.894050545

Find the distance between cities. Assume that Earth's radius is 4000 miles. City 1: 37°47'36''N City 2: 47°37'18''N

686.1471071 mi

Convert to degrees: 5π/11

81.81818182°

Find the arc length s: r=12 cm. θ=135°

9π cm

Find the Amplitude, Period, Phase shift, Vertical shift, and Reflections: y=sin(x-π)

Amplitude: 1 Period: 2π Phase shift: right π Vertical shift: none Reflections: none

Find the Amplitude, Period, Phase shift, Vertical shift, and Reflections: y=sin(x/4)

Amplitude: 1 Period: 8π Phase shift: none Vertical shift: none Reflections: none

Find the Amplitude, Period, Phase shift, Vertical shift, and Reflections: y=-2cos(4πx+1)

Amplitude: 2 Period: 1/2 Phase shift: left 1/(4π) Vertical shift: none Reflections: over the x-axis

Find the Amplitude, Period, Phase shift, Vertical shift, and Reflections: y=2cosx-3

Amplitude: 2 Period: 2π Phase shift: none Vertical shift: down 3 Reflections: none

Find the Amplitude, Period, Phase shift, Vertical shift, and Reflections: y=3cos(x+(π/2))

Amplitude: 3 Period: 2π Phase shift: π/2 Vertical shift: none Reflections: none

Find the Amplitude, Period, Phase shift, Vertical shift, and Reflections: y=3/4cosx

Amplitude: 3/4 Period: 2π Phase shift: none Vertical shift: none Reflections: none

Find the Amplitude, Period, Phase shift, Vertical shift, and Reflections: y=5sinx

Amplitude: 5 Period: 2π Phase shift: none Vertical shift: none Reflections: none

State the quadrant: tanθ>0 and cscθ<0

Quadrant III

State the quadrant: sinθ>0 and cotθ<0

Quadrant IV

Find the other five trig functions: sinθ=3/8

cosθ=(√55)/8 tanθ=3(√55)/55 cscθ=8/3 secθ=8(√55)/55 cotθ=(√55)/3

Evaluate the sine, cosine, and tangent of the angle without using a calculator: -20π/3

sin(-20π/3)=-(√3)/2 cos(-20π/3)=-1/2 tan(-20π/3)=(√3)

Evaluate the sine, cosine, and tangent of the angle without using a calculator: -495°

sin(-495°)=-(√2)/2 cos(-495°)=-(√2)/2 tan(-495°)=1

Evaluate the sine, cosine, and tangent of the angle without using a calculator: -4π/3

sin(-4π/3)=(√3)/2 cos(-4π/3)=-1/2 tan(-4π/3)=-(√3)

Evaluate the sine, cosine, and tangent of the angle without using a calculator: 10π/3

sin10π/3=-(√3)/2 cos10π/3=-1/2 tan10π/3=(√3)

Evaluate the sine, cosine, and tangent of the angle without using a calculator: 300°

sin300°=-(√3)/2 cos300°=1/2 tan300°=-(√3)

Evaluate the sine, cosine, and tangent of the angle without using a calculator: 3π/4

sin3π/4=(√2)/2 cos3π/4=-(√2)/2 tan3π/4=-1

Find the other five trig functions: cotθ=5

sinθ=(√26)/26 cosθ=5(√26)/26 tanθ=1/5 cscθ=(√26) secθ=(√26)/5

Find the remaining trig functions. cotθ=5 sinθ>0

sinθ=(√26)/26 cosθ=5(√26)/26 tanθ=1/5 cscθ=(√26) secθ=(√26)/5

Find the remaining trig functions. secθ=-4/3 cotθ>0

sinθ=-(√7)/4 cosθ=-3/4 tanθ=(√7)/3 cscθ=-4(√7)/7 cotθ=3(√7)/7

Find the six trig functions. Function Value: tanθ is undefined Constraint: π ≤ θ ≤ 2π

sinθ=-1 cosθ=0 tanθ=undefined cscθ=-1 secθ=undefined cotθ=0

Find the six trig functions. Function Value: cosθ=-4/5 Constraint: θ lies in Quadrant III

sinθ=-3/5 cosθ=-4/5 tanθ=3/4 cscθ=-5/3 secθ=-5/4 cotθ=4/3

Find the six trig functions. Function Value: sinθ=0 Constraint: π/2 ≤ θ ≤ 3π/2

sinθ=0 cosθ=-1 tanθ=0 cscθ=undefined secθ=-1 cotθ=undefined

Find the six trig functions. Function Value: cscθ=4 Constraint: cotθ<0

sinθ=1/4 cosθ=-(√15)/4 tanθ=-(√15)/15 cscθ=4 secθ=-4(√15)/15 cotθ=-(√15)

Find the other five trig functions: cosθ=3/7

sinθ=2(√10)/7 tanθ=2(√10)/3 cscθ=7(√10)/20 secθ=7/3 cotθ=3(√10)/20

Find all six trigonometric functions: Opposite=18 Adjacent=12

sinθ=3(√13)/13 cosθ=2(√13)/13 tanθ=3/2 cscθ=(√13)/3 secθ=(√13)/2 cotθ=2/3

Find the other five trig functions: cscθ=17/4

sinθ=4/17 cosθ=(√273)/17 tanθ=4(√273)/273 secθ=17(√273)/273 cotθ=(√273)/4

Find all six trigonometric functions: Opposite=5 Hypotenuse=13

sinθ=5/13 cosθ=12/13 tanθ=5/12 cscθ=13/5 secθ=13/12 cotθ=12/5

Find reference angle: 10π/3

π/3

Find the reference angle: -5π/3

π/3

Find the reference angle: 3π/4

π/4

Find the reference angle: 7π/6

π/6