Question 1

Verify the identity.

Accepted Answer

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

Question 2

Find the exact values of   for the given conditions.

Accepted Answer

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

Question 3

Find the identity for the function.

Accepted Answer

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

Question 4

Shown in the figure is a graph of the function f for   . Use a sum-to-product formula to help find the first two x-intercepts.

Accepted Answer

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

Question 5

Find all solutions of the equation.

Accepted Answer

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

Question 6

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 7

A golfer, centered in a b = 20-yard-wide straight fairway, hits a ball a = 270 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.

Accepted Answer

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

Question 8

Tell whether the reduction formula is correct or incorrect.

Accepted Answer

A) correct 
B) incorrect 
A) correct 
B) incorrect

Question 9

Shown in the figure is a graph of the function f for   . Use a sum-to-product formula to help find the first two x-intercepts.

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

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 12

A golfer, centered in a b = 40-yard-wide straight fairway, hits a ball a = 230 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.

Accepted Answer

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

Question 13

Find all solutions of the equation.

Accepted Answer

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

Question 14

Express as a sum or difference.

Accepted Answer

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

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

Verify the identity.

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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 19

Express as a sum or difference.

Accepted Answer

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

Question 20

Verify the identity.

Accepted Answer

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

Verify the identity.

Find the exact values of for the given conditions.

Find the identity for the function.

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.

Find all solutions of the equation.

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

A golfer, centered in a b = 20-yard-wide straight fairway, hits a ball a = 270 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.

Tell whether the reduction formula is correct or incorrect.

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.

Verify the identity.

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

A golfer, centered in a b = 40-yard-wide straight fairway, hits a ball a = 230 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.

Find all solutions of the equation.

Express as a sum or difference.

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

Verify the identity.

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

Express as a sum or difference.

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

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Exam 7: Analytic Trigonometry

Verify the identity.

Find the exact values of for the given conditions.

Find the identity for the function.

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.

Find all solutions of the equation.

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

A golfer, centered in a b = 20-yard-wide straight fairway, hits a ball a = 270 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.

Tell whether the reduction formula is correct or incorrect.

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.

Verify the identity.

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

A golfer, centered in a b = 40-yard-wide straight fairway, hits a ball a = 230 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.

Find all solutions of the equation.

Express as a sum or difference.

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

Verify the identity.

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

Express as a sum or difference.

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 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.