Exam 1: Trigonometry

A television camera at ground level is filming the lift-off of a space shuttle at a point meters from the launch pad (see figure).Let θ be the angle of elevation to the shuttle and let s be the height of the shuttle.Write θ as a function of s.

(Multiple Choice)

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Question 161

Find the value of given trigonometric function.Round your answer to four decimal places.

(Multiple Choice)

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Question 162

Evaluate without using a calculator.

(Multiple Choice)

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Question 163

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when .

(Multiple Choice)

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Question 164

For the simple harmonic motion described by the trigonometric function, find the frequency per second.

(Multiple Choice)

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Question 165

Determine two coterminal angles (one positive and one negative) for .

(Multiple Choice)

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Question 166

The point (-7,-24) is on the terminal side of an angle in standard position.Determine the exact value of .

(Multiple Choice)

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Question 167

Given the equation below, determine two solutions such that . sec θ =

(Multiple Choice)

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Question 168

Determine the exact value of when and .

(Multiple Choice)

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Question 169

Select the graph of the function below.Include two full periods.

(Multiple Choice)

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Question 170

The point (7, 24) is on the terminal side of an angle in standard position.Determine the exact value of cos θ.

(Multiple Choice)

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Question 171

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down units.

(Multiple Choice)

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Question 172

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze, the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity.

(Multiple Choice)

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Question 173

You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 130 feet ahead of the balloon (see figure). Find an expression for the angle of elevation from you to the top of the balloon.

(Multiple Choice)

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Question 174

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.

(Multiple Choice)

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Question 175

Use an inverse trigonometric function to write θ as a function of x. A = x B = 10

(Multiple Choice)

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Question 176

State the period of the function:

(Multiple Choice)

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Question 177

Find the length of the sides of a regular pentagon inscribed in a circle of radius 26 inches.Round your answer to one decimal place.

(Multiple Choice)

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Question 178

A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches.Its motion (in ideal conditions) is modeled by where y is measured in feet and t is the time in seconds. What is the period of the oscillations?

(Multiple Choice)

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Question 179

Evaluate (if possible) the sine, cosine, and tangent of the real number.

(Multiple Choice)

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Question 180

Showing 161 - 180 of 393

A television camera at ground level is filming the lift-off of a space shuttle at a point meters from the launch pad (see figure).Let θ be the angle of elevation to the shuttle and let s be the height of the shuttle.Write θ as a function of s.

Find the value of given trigonometric function.Round your answer to four decimal places.

Evaluate without using a calculator.

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when .

For the simple harmonic motion described by the trigonometric function, find the frequency per second.

Determine two coterminal angles (one positive and one negative) for .

The point (-7,-24) is on the terminal side of an angle in standard position.Determine the exact value of .

Given the equation below, determine two solutions such that . sec θ =

Determine the exact value of when and .

Select the graph of the function below.Include two full periods.

The point (7, 24) is on the terminal side of an angle in standard position.Determine the exact value of cos θ.

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down units.

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze, the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity.

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.

Use an inverse trigonometric function to write θ as a function of x. A = x B = 10

State the period of the function:

Find the length of the sides of a regular pentagon inscribed in a circle of radius 26 inches.Round your answer to one decimal place.

A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches.Its motion (in ideal conditions) is modeled by where y is measured in feet and t is the time in seconds. What is the period of the oscillations?

Evaluate (if possible) the sine, cosine, and tangent of the real number.

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

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Exam 1: Trigonometry

A television camera at ground level is filming the lift-off of a space shuttle at a point meters from the launch pad (see figure).Let θ be the angle of elevation to the shuttle and let s be the height of the shuttle.Write θ as a function of s. ​ ​

Find the value of given trigonometric function.Round your answer to four decimal places. ​ ​

Evaluate without using a calculator.

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when . ​

For the simple harmonic motion described by the trigonometric function, find the frequency per second. ​ ​

Determine two coterminal angles (one positive and one negative) for .

The point (-7,-24) is on the terminal side of an angle in standard position.Determine the exact value of .

Given the equation below, determine two solutions such that . sec​ θ = ​

Determine the exact value of when and .

Select the graph of the function below.Include two full periods. ​ ​

The point (7, 24) is on the terminal side of an angle in standard position.Determine the exact value of cos θ.

Write an equation for the function that is described by the given characteristics. ​ A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down units. ​

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze, the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity. ​

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window. ​ ​

Use an inverse trigonometric function to write θ as a function of x. ​ ​ A = x B = 10 ​

State the period of the function: ​ ​

Find the length of the sides of a regular pentagon inscribed in a circle of radius 26 inches.Round your answer to one decimal place. ​

A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches.Its motion (in ideal conditions) is modeled by ​ where y is measured in feet and t is the time in seconds. What is the period of the oscillations? ​

Evaluate (if possible) the sine, cosine, and tangent of the real number. ​ ​

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

A television camera at ground level is filming the lift-off of a space shuttle at a point meters from the launch pad (see figure).Let θ be the angle of elevation to the shuttle and let s be the height of the shuttle.Write θ as a function of s.

Find the value of given trigonometric function.Round your answer to four decimal places.

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement (in feet) and t is the time (in seconds).Find the displacements when .

For the simple harmonic motion described by the trigonometric function, find the frequency per second.

Given the equation below, determine two solutions such that . sec θ =

Select the graph of the function below.Include two full periods.

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of π, an amplitude of 6, a left phase shift of π, and a vertical translation down units.

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze, the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity.

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.

Use an inverse trigonometric function to write θ as a function of x. A = x B = 10

State the period of the function:

Find the length of the sides of a regular pentagon inscribed in a circle of radius 26 inches.Round your answer to one decimal place.

A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches.Its motion (in ideal conditions) is modeled by where y is measured in feet and t is the time in seconds. What is the period of the oscillations?

Evaluate (if possible) the sine, cosine, and tangent of the real number.