Question 1

Graph the function by first writing it in the form y = A sin(x + C). State the amplitude, period, and phase shift.
-y = 4 sin x - 4 cos x

Accepted Answer

A)    ,phase shift     
B)    ,phase shift     
C)    period 2   ,phase shift     
D)    , period 2   ,phase shift -     
A)    ,phase shift     
B)    ,phase shift     
C)    period 2   ,phase shift     
D)    , period 2   ,phase shift -

Question 2

Use an appropriate identity to find the exact value of the expression.
-

Accepted Answer

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

Question 3

Use a sum-to-product identity to rewrite the expression.
-cos 56° + cos 28°

Accepted Answer

A)  2 cos 42° sin 14° 
B)  -2 sin 42° sin 14° 
C)  2 sin 42° cos 14° 
D)  2 cos 42° cos 14° 
A)  2 cos 42° sin 14° 
B)  -2 sin 42° sin 14° 
C)  2 sin 42° cos 14° 
D)  2 cos 42° cos 14°

Question 4

Find the exact value by using a half-angle identity.
-sin

Accepted Answer

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

Question 5

Complete the equation so the result is an identity.
-

Accepted Answer

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

Question 6

Identify the equation as either an identity or not.
-2 sin 5x cos x = sin 6x + sin 4x

Accepted Answer

A)  Not an identity 
B)  Identity 
A)  Not an identity 
B)  Identity

Question 7

Use trigonometric identities to find the exact value.
-

Accepted Answer

A)    
B)  -2 
C)    
D)    
A)    
B)  -2 
C)    
D)

Question 8

Find the exact value by using a half-angle identity.
-cos 22.5°

Accepted Answer

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

Question 9

Use the appropriate sum or difference identity to write the given expression as a function of x alone.
-sin (180° + x)

Accepted Answer

A)  cos x 
B)  sin x 
C)  - sin x 
D)  - cos x 
A)  cos x 
B)  sin x 
C)  - sin x 
D)  - cos x

Question 10

Use trigonometric identities to find the exact value.
-

Accepted Answer

A)    
B)    
C)    
D)  -2 
A)    
B)    
C)    
D)  -2

Question 11

Find the exact value by using a sum or difference identity.
-tan (165°)

Accepted Answer

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

Question 12

Solve the problem.
-The area of a triangle is given by   where a and b are the lengths of two of the sides and C is the included angle. If A =   a = 5 in., b = 8 in., and C is an acute angle, what must C be? Give your answer in degrees to the nearest hundredth.

Accepted Answer

A)  108.19° 
B)  71.81° 
C)  35.90° 
D)  No such triangle exists. 
A)  108.19° 
B)  71.81° 
C)  35.90° 
D)  No such triangle exists.

Question 13

Use an appropriate identity to find the exact value of the expression.
-

Accepted Answer

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

Question 14

Use identities to find the exact value of the trigonometric function.
-Find cot   if csc

Accepted Answer

A)  5 
B)    
C)    
D)    
A)  5 
B)    
C)    
D)

Question 15

Find the exact value of the expression using the provided information.
-Find cos(A + B)   , with A in quadrant I, and sin   , with B in quadrant IV.

Accepted Answer

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

Question 16

Choose the equivalent expression for the given expression.
-

Accepted Answer

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

Question 17

Find the exact value by using a half-angle identity.
-cos

Accepted Answer

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

Question 18

For the following equation, graph   on the same screen on your calculator. From the graphs, make
a conjecture as to whether the equation is an identity. If so, prove your conjecture.
-

Accepted Answer

The statement is an

Question 19

Decide whether the expression is or is not an identity.
-  = csc x

Accepted Answer

A)  Identity 
B)  Not an identity 
A)  Identity 
B)  Not an identity

Question 20

Write in terms of the cofunction of a complementary angle.
-cos 19°

Accepted Answer

A)  sin 161° 
B)  sec 161° 
C)  sin 71° 
D)  sec 71° 
A)  sin 161° 
B)  sec 161° 
C)  sin 71° 
D)  sec 71°

Graph the function by first writing it in the form y = A sin(x + C). State the amplitude, period, and phase shift. -y = 4 sin x - 4 cos x

Use an appropriate identity to find the exact value of the expression. -

Use a sum-to-product identity to rewrite the expression. -cos 56° + cos 28°

Find the exact value by using a half-angle identity. -sin

Complete the equation so the result is an identity. -

Identify the equation as either an identity or not. -2 sin 5x cos x = sin 6x + sin 4x

Use trigonometric identities to find the exact value. -

Find the exact value by using a half-angle identity. -cos 22.5°

Use the appropriate sum or difference identity to write the given expression as a function of x alone. -sin (180° + x)

Use trigonometric identities to find the exact value. -

Find the exact value by using a sum or difference identity. -tan (165°)

Solve the problem. -The area of a triangle is given by where a and b are the lengths of two of the sides and C is the included angle. If A = a = 5 in., b = 8 in., and C is an acute angle, what must C be? Give your answer in degrees to the nearest hundredth.

Use an appropriate identity to find the exact value of the expression. -

Use identities to find the exact value of the trigonometric function. -Find cot if csc

Find the exact value of the expression using the provided information. -Find cos(A + B) , with A in quadrant I, and sin , with B in quadrant IV.

Choose the equivalent expression for the given expression. -

Find the exact value by using a half-angle identity. -cos

For the following equation, graph on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -

Decide whether the expression is or is not an identity. - = csc x

Write in terms of the cofunction of a complementary angle. -cos 19°

Equations, Inequalities, and Modeling

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

The Conic Sections

Sequences, Series, and Probability

Basic Algebra Review

Filters

Exam 6: Trigonometric Identities and Conditional Equations

Graph the function by first writing it in the form y = A sin(x + C). State the amplitude, period, and phase shift. -y = 4 sin x - 4 cos x

Use an appropriate identity to find the exact value of the expression. -

Use a sum-to-product identity to rewrite the expression. -cos 56° + cos 28°

Find the exact value by using a half-angle identity. -sin

Complete the equation so the result is an identity. -

Identify the equation as either an identity or not. -2 sin 5x cos x = sin 6x + sin 4x

Use trigonometric identities to find the exact value. -

Find the exact value by using a half-angle identity. -cos 22.5°

Use the appropriate sum or difference identity to write the given expression as a function of x alone. -sin (180° + x)

Use trigonometric identities to find the exact value. -

Find the exact value by using a sum or difference identity. -tan (165°)

Solve the problem. -The area of a triangle is given by where a and b are the lengths of two of the sides and C is the included angle. If A = a = 5 in., b = 8 in., and C is an acute angle, what must C be? Give your answer in degrees to the nearest hundredth.

Use an appropriate identity to find the exact value of the expression. -

Use identities to find the exact value of the trigonometric function. -Find cot if csc

Find the exact value of the expression using the provided information. -Find cos(A + B) , with A in quadrant I, and sin , with B in quadrant IV.

Choose the equivalent expression for the given expression. -

Find the exact value by using a half-angle identity. -cos

For the following equation, graph on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -

Decide whether the expression is or is not an identity. - = csc x

Write in terms of the cofunction of a complementary angle. -cos 19°

Equations, Inequalities, and Modeling

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

The Conic Sections

Sequences, Series, and Probability

Basic Algebra Review

Filters