Question 1

Solve right triangle ABC if A = 67° and c = 22.1 ft. Round lengths to one decimal point.

Accepted Answer

A)  a = 8.6 ft, b = 20.3 ft, B = 23° 
B)  a = 20.3 ft, b = 8.6 ft, B = 23° 
C)  a = 20.3 ft, b = 52.06 ft, B = 113° 
D)  a = 52.06 ft, b = 8.6 ft, B = 113° 
A)  a = 8.6 ft, b = 20.3 ft, B = 23° 
B)  a = 20.3 ft, b = 8.6 ft, B = 23° 
C)  a = 20.3 ft, b = 52.06 ft, B = 113° 
D)  a = 52.06 ft, b = 8.6 ft, B = 113°

Question 2

Solve the given triangle and round to one decimal place.
 
B = 33.0 in., c = 35.8 in., $\beta$ = 30.0°

Accepted Answer

A)  Case one: $\gamma$1 = 32.8°, $\alpha$1 = 117.2°, a1 = 58.7 in.
Case two: $\gamma$2 = 147.2°, $\alpha$2 = 2.8°, a2 = 3.3 in. 
B)  Case one: $\gamma$1 = 32.8°, $\alpha$1 = 117.2°, a1 = 58.7 in.
Case two: $\gamma$2 = 2.8°, $\alpha$2 = 147.2°, a2 = 3.3 in. 
C)  $\gamma$ = 32.8°, $\alpha$= 117.2°, a = 58.7 in. and no ambiguous case 
D)  no solution 
A)  Case one: $\gamma$1 = 32.8°, $\alpha$1 = 117.2°, a1 = 58.7 in.
Case two: $\gamma$2 = 147.2°, $\alpha$2 = 2.8°, a2 = 3.3 in. 
B)  Case one: $\gamma$1 = 32.8°, $\alpha$1 = 117.2°, a1 = 58.7 in.
Case two: $\gamma$2 = 2.8°, $\alpha$2 = 147.2°, a2 = 3.3 in. 
C)  $\gamma$ = 32.8°, $\alpha$= 117.2°, a = 58.7 in. and no ambiguous case 
D)  no solution

Question 3

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 28° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 39°, then how long is the slide?

Accepted Answer

The answer of An airplane door is 5 feet high....

Question 4

Indicate the quadrant in which the terminal side of θ must lie in order for the following to be true:
sinθ is positive and tanθ is negative.

Accepted Answer

The answer of Indicate the quadrant in which the terminal...

Question 5

Use the triangle to find the exact sinθ. Rationalize the denominator and reduce the fraction if necessary.

Accepted Answer

The answer of Use the triangle to find the exact...

Question 6

State in which quadrant or on what axis the terminal side of a 1215° angle in standard position lies.

Accepted Answer

A)  QI 
B)  QII 
C)  QIII 
D)  x-axis 
A)  QI 
B)  QII 
C)  QIII 
D)  x-axis

Question 7

Find the exact length of the arc subtended by a central angle of $\theta$ = 
   
on a circle with radius 32 m.

Accepted Answer

The answer of Find the exact length of the arc...

Question 8

Bearing (Navigation). If a plane takes off bearing N 71° W and flies 5 miles and then makes a right turn (90°) and flies 14 miles further, what bearing will the traffic controller use to locate the plane?

Accepted Answer

A)  N 1° E 
B)  N 1° W 
C)  N 70° E 
D)  N 70° W 
A)  N 1° E 
B)  N 1° W 
C)  N 70° E 
D)  N 70° W

Question 9

The terminal side of an angle θ in standard position passes through the point 
   
. Calculate the value of cot θ.

Accepted Answer

The answer of The terminal side of an angle θ...

Question 10

If cos θ = 
   
, and the terminal side of θ lies in quadrant I, find sin θ.

Accepted Answer

The answer of If cos θ = 
  ...

Question 11

Light rays that hit the surface of water are bent, or refracted, according to Snell's Law:
n1sin θ1 = n2sin θ2.
Find the refraction index of water n2 if the angle of refraction of water θ2 = 26°, the refraction index of air n1 = 1, and light enters the water at an angle θ1 = 36°. Round your answer to 1 decimal place.

Accepted Answer

Question 12

Glide Path of a Commercial Jet Airliner. If a commercial jetliner is at an altitude of 330 feet when it is 7100 feet from the runway, what is the glide slope angle$\theta$ will the pilot see white lights, red lights, or both? Round to tenth of a degree.

Accepted Answer

The answer of Glide Path of a Commercial Jet Airliner....

Question 13

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 281 feet and 253 feet. The angle between the two sides is 57°. What is the area of the parking lot? Round to the nearest integer.

Accepted Answer

A)  59,624 square feet 
B)  29,812 square feet 
C)  31,008 square feet 
D)  38,720 square feet 
A)  59,624 square feet 
B)  29,812 square feet 
C)  31,008 square feet 
D)  38,720 square feet

Question 14

Find the angular speed,
 
, associated with rotating a central angle $\theta$ =
 
In time t = 10 seconds.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Find the positive measure of $\theta$ (rounded to the nearest degree) if tan $\theta$ =
 
And the terminal side of $\theta$ lies in quadrant II.

Accepted Answer

A)  95° 
B)  185° 
C)  355° 
D)  5° 
A)  95° 
B)  185° 
C)  355° 
D)  5°

Question 16

The terminal side of an angle θ in standard position passes through the point 
   
. Calculate the value of csc θ.

Accepted Answer

The answer of The terminal side of an angle θ...

Question 17

Find the positive measure of $\theta$ (rounded to the nearest degree) if cos$\theta$ =
 
And the terminal side of $\theta$ lies in quadrant IV.

Accepted Answer

A)  51° 
B)  219° 
C)  141° 
D)  309° 
A)  51° 
B)  219° 
C)  141° 
D)  309°

Question 18

Use a calculator to approximate the csc 31.5° to three decimal places.

Accepted Answer

A)  0.853 
B)  1.632 
C)  0.522 
D)  1.914 
A)  0.853 
B)  1.632 
C)  0.522 
D)  1.914

Question 19

The terminal side of an angle θ in standard position passes through the point 
   
. Calculate the value of sec θ.

Accepted Answer

The answer of The terminal side of an angle θ...

Question 20

Use a calculator to approximate the length of the arc on a circle with central angle $\theta$ = 125° and radius r = 10 km.

Accepted Answer

A)  22 km. 
B)  6 km 
C)  11 km 
D)  22 km 
A)  22 km. 
B)  6 km 
C)  11 km 
D)  22 km

Solve right triangle ABC if A = 67° and c = 22.1 ft. Round lengths to one decimal point.

Solve the given triangle and round to one decimal place. $Solve the given triangle and round to one decimal place. B = 33.0 in., c = 35.8 in., \beta = 30.0°$ B = 33.0 in., c = 35.8 in., $\beta$ = 30.0°

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 28° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 39°, then how long is the slide?

Indicate the quadrant in which the terminal side of θ must lie in order for the following to be true: sinθ is positive and tanθ is negative.

Use the triangle to find the exact sinθ. Rationalize the denominator and reduce the fraction if necessary. $Use the triangle to find the exact sinθ. Rationalize the denominator and reduce the fraction if necessary.$

State in which quadrant or on what axis the terminal side of a 1215° angle in standard position lies.

Find the exact length of the arc subtended by a central angle of $\theta$ = $Find the exact length of the arc subtended by a central angle of \theta = on a circle with radius 32 m.$ on a circle with radius 32 m.

Bearing (Navigation). If a plane takes off bearing N 71° W and flies 5 miles and then makes a right turn (90°) and flies 14 miles further, what bearing will the traffic controller use to locate the plane?

The terminal side of an angle θ in standard position passes through the point . Calculate the value of cot θ.

If cos θ = , and the terminal side of θ lies in quadrant I, find sin θ.

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 281 feet and 253 feet. The angle between the two sides is 57°. What is the area of the parking lot? Round to the nearest integer.

Find the positive measure of $\theta$ (rounded to the nearest degree) if tan $\theta$ = $Find the positive measure of \theta (rounded to the nearest degree) if tan \theta = And the terminal side of \theta lies in quadrant II.$ And the terminal side of $\theta$ lies in quadrant II.

The terminal side of an angle θ in standard position passes through the point . Calculate the value of csc θ.

Find the positive measure of $\theta$ (rounded to the nearest degree) if cos $\theta$ = $Find the positive measure of \theta (rounded to the nearest degree) if cos \theta = And the terminal side of \theta lies in quadrant IV.$ And the terminal side of $\theta$ lies in quadrant IV.

Use a calculator to approximate the csc 31.5° to three decimal places.

The terminal side of an angle θ in standard position passes through the point . Calculate the value of sec θ.

Use a calculator to approximate the length of the arc on a circle with central angle $\theta$ = 125° and radius r = 10 km.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions of Real Numbers

Analytic Trigonometry

Vectors, the Complex Plane, and Polar Coordinates

Systems of Linear Equations and Inequalities

Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

Sequences and Series

Limits: A Preview to Calculus

Review: Equations and Inequalities

Filters

Exam 4: Trigonometric Functions of Angles

Solve right triangle ABC if A = 67° and c = 22.1 ft. Round lengths to one decimal point.

Solve the given triangle and round to one decimal place. B = 33.0 in., c = 35.8 in., β\betaβ = 30.0°

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 28° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 39°, then how long is the slide?

Indicate the quadrant in which the terminal side of θ must lie in order for the following to be true: sinθ is positive and tanθ is negative.

Use the triangle to find the exact sinθ. Rationalize the denominator and reduce the fraction if necessary.

State in which quadrant or on what axis the terminal side of a 1215° angle in standard position lies.

Find the exact length of the arc subtended by a central angle of θ\thetaθ = on a circle with radius 32 m.

Bearing (Navigation). If a plane takes off bearing N 71° W and flies 5 miles and then makes a right turn (90°) and flies 14 miles further, what bearing will the traffic controller use to locate the plane?

The terminal side of an angle θ in standard position passes through the point . Calculate the value of cot θ.

If cos θ = , and the terminal side of θ lies in quadrant I, find sin θ.

Glide Path of a Commercial Jet Airliner. If a commercial jetliner is at an altitude of 330 feet when it is 7100 feet from the runway, what is the glide slope angle θ\thetaθ will the pilot see white lights, red lights, or both? Round to tenth of a degree.

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 281 feet and 253 feet. The angle between the two sides is 57°. What is the area of the parking lot? Round to the nearest integer.

Find the angular speed, , associated with rotating a central angle θ\thetaθ = In time t = 10 seconds.

Find the positive measure of θ\thetaθ (rounded to the nearest degree) if tan θ\thetaθ = And the terminal side of θ\thetaθ lies in quadrant II.

The terminal side of an angle θ in standard position passes through the point . Calculate the value of csc θ.

Find the positive measure of θ\thetaθ (rounded to the nearest degree) if cos θ\thetaθ = And the terminal side of θ\thetaθ lies in quadrant IV.

Use a calculator to approximate the csc 31.5° to three decimal places.

The terminal side of an angle θ in standard position passes through the point . Calculate the value of sec θ.

Use a calculator to approximate the length of the arc on a circle with central angle θ\thetaθ = 125° and radius r = 10 km.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions of Real Numbers

Analytic Trigonometry

Vectors, the Complex Plane, and Polar Coordinates

Systems of Linear Equations and Inequalities

Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

Sequences and Series

Limits: A Preview to Calculus

Review: Equations and Inequalities

Filters

Solve the given triangle and round to one decimal place. $Solve the given triangle and round to one decimal place. B = 33.0 in., c = 35.8 in., \beta = 30.0°$ B = 33.0 in., c = 35.8 in., $\beta$ = 30.0°

Use the triangle to find the exact sinθ. Rationalize the denominator and reduce the fraction if necessary. $Use the triangle to find the exact sinθ. Rationalize the denominator and reduce the fraction if necessary.$

Find the exact length of the arc subtended by a central angle of $\theta$ = $Find the exact length of the arc subtended by a central angle of \theta = on a circle with radius 32 m.$ on a circle with radius 32 m.

Find the positive measure of $\theta$ (rounded to the nearest degree) if tan $\theta$ = $Find the positive measure of \theta (rounded to the nearest degree) if tan \theta = And the terminal side of \theta lies in quadrant II.$ And the terminal side of $\theta$ lies in quadrant II.

Find the positive measure of $\theta$ (rounded to the nearest degree) if cos $\theta$ = $Find the positive measure of \theta (rounded to the nearest degree) if cos \theta = And the terminal side of \theta lies in quadrant IV.$ And the terminal side of $\theta$ lies in quadrant IV.

Use a calculator to approximate the length of the arc on a circle with central angle $\theta$ = 125° and radius r = 10 km.