Question 1

Verify the identity.

Accepted Answer

A) Identical 
B) Not identical 
A) Identical 
B) Not identical

Question 2

Use sum-to-product formulas to find the solutions of the equation.

Accepted Answer

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

Question 3

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 4

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula   where D is the depth (in kilometers) below the surface of the focal point of the earthquake. Approximate the depth D of the focal point of an earthquake with S = 5 m if a point on the surface of Earth 7 kilometers from the fault line moved 0.67 meters horizontally. Round the answer to the nearest hundredth.

Accepted Answer

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

Question 5

Find all solutions of the equation.

Accepted Answer

A)    and   for every integer n. 
B)    and   for every integer n. 
C)    and   for every integer n. 
D)    for every integer n. 
E)    and   for every integer n. 
A)    and   for every integer n. 
B)    and   for every integer n. 
C)    and   for every integer n. 
D)    for every integer n. 
E)    and   for every integer n.

Question 6

Verify the identity.

Accepted Answer

A) Not identical 
B) Identical 
A) Not identical 
B) Identical

Question 7

Find the exact value.

Accepted Answer

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

Question 8

Find the exact values of   for the given values of   .

Accepted Answer

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

Question 9

Use the graph of f to find the simplest expression g(x) such that the equation   is an identity.

Accepted Answer

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

Question 10

Express as a cofunction of a complementary angle.

Accepted Answer

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

Question 11

Verify the identity.

Accepted Answer

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

Question 12

Find all solutions of the equation.

Accepted Answer

A)    for every integer n. 
B)    for every integer n. 
C) 1 
D)    for every integer n. 
E)    for every integer n. 
A)    for every integer n. 
B)    for every integer n. 
C) 1 
D)    for every integer n. 
E)    for every integer n.

Question 13

On a clear 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 14

Verify the identity.

Accepted Answer

A) Not identical 
B) Identical 
A) Not identical 
B) Identical

Question 15

If   and   for a second-quadrant angle   and a third-quadrant angle   , find

Accepted Answer

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

Question 16

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 November.

Accepted Answer

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

Question 17

Find the exact value of the expression.

Accepted Answer

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

Question 18

Verify the identity.

Accepted Answer

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

Question 19

Express as a cofunction of a complementary angle.

Accepted Answer

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

Question 20

Verify the identity.

Accepted Answer

A) Not identical 
B) Identical 
A) Not identical 
B) Identical

Verify the identity.

Use sum-to-product formulas to find the solutions of the equation.

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

Find all solutions of the equation.

Verify the identity.

Find the exact value.

Find the exact values of for the given values of .

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.

Express as a cofunction of a complementary angle.

Verify the identity.

Find all solutions of the equation.

On a clear 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.

If and for a second-quadrant angle and a third-quadrant angle , find

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 November.

Find the exact value of the expression.

Verify the identity.

Express as a cofunction of a complementary angle.

Verify the identity.

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

Verify the identity.

Use sum-to-product formulas to find the solutions of the equation.

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

Find all solutions of the equation.

Verify the identity.

Find the exact value.

Find the exact values of for the given values of .

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.

Express as a cofunction of a complementary angle.

Verify the identity.

Find all solutions of the equation.

On a clear 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.

If and for a second-quadrant angle and a third-quadrant angle , find

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 November.

Find the exact value of the expression.

Verify the identity.

Express as a cofunction of a complementary angle.

Verify the identity.

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 clear 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.