Question 1

A graph of   for   is shown in the figure. Find the exact values of the x-intercepts.

Accepted Answer

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

Question 2

Use the formula     to determine the amplitude of f (x).

Accepted Answer

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

Question 3

Use an addition or subtraction formula to find the solutions of the equation that are in the interval   .

Accepted Answer

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

Question 4

Verify the identity.

Accepted Answer

A) invalid 
B) valid 
A) invalid 
B) valid

Question 5

Verify the identity.

Accepted Answer

A) valid 
B) invalid 
A) valid 
B) invalid

Question 6

Find the solutions of the equation that are in the interval

Accepted Answer

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

Question 7

Use the formula     to determine the period of f (x).

Accepted Answer

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

Question 8

The average monthly high temperature T (in   ) in Augusta, Georgia, can be approximated using the function   where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.

Accepted Answer

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

Question 9

Use the formula     to determine the period of f (x).

Accepted Answer

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

Question 10

Verify the identity.

Accepted Answer

A) valid 
B) invalid 
A) valid 
B) invalid

Question 11

Find the exact value.

Accepted Answer

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

Question 12

Express as a product.

Accepted Answer

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

Question 13

Make the trigonometric substitution   and a > 0. Use fundamental identities to simplify the resulting expression.

Accepted Answer

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

Question 14

Find the exact value of the expression.

Accepted Answer

A)    
B) 0 
C)    
D) 1 
E)    
A)    
B) 0 
C)    
D) 1 
E)

Question 15

If a mass that is attached to a spring is raised y 0  feet and released with an initial vertical velocity of v 0  ft / sec, then the subsequent position y of the mass is given by   where t is time in seconds and   is a positive constant. If y 0  = 2 and   = 2, find the initial velocities that result in an amplitude of 4 feet.

Accepted Answer

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

Question 16

Verify the identity.

Accepted Answer

A) invalid 
B) valid 
A) invalid 
B) valid

Question 17

On a cloudy day with D hours of daylight, the intensity of sunlight I (in calories/cm 2 ) may be approximated by   where t = 0 corresponds to sunrise and I m  is the maximum intensity. If D = 12, approximately how many hours after sunrise is   ? Round your answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Question 18

Verify the identity.

Accepted Answer

A) valid 
B) invalid 
A) valid 
B) invalid

Question 19

Verify the identity.

Accepted Answer

A) valid 
B) invalid 
A) valid 
B) invalid

Question 20

The average monthly high temperature T (in   ) in Augusta, Georgia, can be approximated using the function   where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.

Accepted Answer

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

A graph of for is shown in the figure. Find the exact values of the x-intercepts.

Use the formula to determine the amplitude of f (x).

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .

Verify the identity.

Verify the identity.

Find the solutions of the equation that are in the interval

Use the formula to determine the period of f (x).

The average monthly high temperature T (in ) in Augusta, Georgia, can be approximated using the function where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.

Use the formula to determine the period of f (x).

Verify the identity.

Find the exact value.

Express as a product.

Make the trigonometric substitution and a > 0. Use fundamental identities to simplify the resulting expression.

Find the exact value of the expression.

Verify the identity.

On a cloudy day with D hours of daylight, the intensity of sunlight I (in calories/cm²) may be approximated by where t = 0 corresponds to sunrise and I_m is the maximum intensity. If D = 12, approximately how many hours after sunrise is ? Round your answer to two decimal places.

Verify the identity.

Verify the identity.

The average monthly high temperature T (in ) in Augusta, Georgia, can be approximated using the function where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Exam 7: Analytic Trigonometry

A graph of for is shown in the figure. Find the exact values of the x-intercepts.

Use the formula to determine the amplitude of f (x).

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .

Verify the identity.

Verify the identity.

Find the solutions of the equation that are in the interval

Use the formula to determine the period of f (x).

The average monthly high temperature T (in ) in Augusta, Georgia, can be approximated using the function where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.

Use the formula to determine the period of f (x).

Verify the identity.

Find the exact value.

Express as a product.

Make the trigonometric substitution and a > 0. Use fundamental identities to simplify the resulting expression.

Find the exact value of the expression.

Verify the identity.

On a cloudy day with D hours of daylight, the intensity of sunlight I (in calories/cm 2 ) may be approximated by where t = 0 corresponds to sunrise and I m is the maximum intensity. If D = 12, approximately how many hours after sunrise is ? Round your answer to two decimal places.

Verify the identity.

Verify the identity.

The average monthly high temperature T (in ) in Augusta, Georgia, can be approximated using the function where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

On a cloudy day with D hours of daylight, the intensity of sunlight I (in calories/cm²) may be approximated by where t = 0 corresponds to sunrise and I_m is the maximum intensity. If D = 12, approximately how many hours after sunrise is ? Round your answer to two decimal places.