Question 1

Find the exact value using a double-angle identity.
-sin(480°)

Accepted Answer

A)    
B)    
C)  -1 
D)    
A)    
B)    
C)  -1 
D)

Question 2

Prove the identity.
-

Accepted Answer

The answer of Prove the identity.
- ...

Question 3

Use identities to find the exact value of the trigonometric function.
-Find sec   given that sin   is in quadrant II.

Accepted Answer

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

Question 4

Find the exact value using a double-angle identity.
-cos

Accepted Answer

A)  0 
B)  -1 
C)  1 
D)    
A)  0 
B)  -1 
C)  1 
D)

Question 5

Find the exact value by using a half-angle identity.
-cos 75°

Accepted Answer

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

Question 6

Show that the equation is not an identity by listing the value(s) of the variable from among   for which
the equation is false.
-sin   + cos   = tan

Accepted Answer

A)  0 
B)    
C)    
D)    
A)  0 
B)    
C)    
D)

Question 7

Use a sum or difference identity to find the exact value.
-sin

Accepted Answer

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

Question 8

Use a product-to-sum identity to rewrite the expression.
-

Accepted Answer

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

Question 9

Use a sum-to-product identity to rewrite the expression.
-sin 43° + sin 55°

Accepted Answer

A)  -2 sin 49° sin 6° 
B)  2 cos 49° cos 6° 
C)  2 sin 49° cos 6° 
D)  2 cos 49° sin 6° 
A)  -2 sin 49° sin 6° 
B)  2 cos 49° cos 6° 
C)  2 sin 49° cos 6° 
D)  2 cos 49° sin 6°

Question 10

Use an identity to write the expression as a single trigonometric function or as a single number.
-

Accepted Answer

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

Question 11

Use identities to find the exact value of the trigonometric function.
-Find sin   if tan

Accepted Answer

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

Question 12

Identify the equation as either an identity or not.
-  = (csc x - 1)(csc x + 1)

Accepted Answer

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

Question 13

Identify the equation as either an identity or not.
-sin   = sin A

Accepted Answer

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

Question 14

Prove that the equation is an identity.
-tan x csc x = csc x

Accepted Answer

The answer of Prove that the equation is an identity.
-tan...

Question 15

Prove that the equation is an identity.
-

Accepted Answer

The answer of Prove that the equation is an identity.
-...

Question 16

Show that the equation is not an identity by listing the value(s) of the variable from among   for which
the equation is false.
-

Accepted Answer

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

Question 17

Solve the problem. Round to the nearest whole unit.
-A balloon rises from a point whose horizontal distance from an observer is d yards. Find an exact expression in terms of d for the distance between the 2 positions of the balloon which correspond to the angles of elevation 15°
And 30° measured from the observer.

Accepted Answer

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

Question 18

Prove that the equation is an identity.
-

Accepted Answer

The answer of Prove that the equation is an identity.
-...

Question 19

Determine whether the positive or negative sign makes the equation correct.
-tan

Accepted Answer

A)  Negative sign 
B)  Positive sign 
A)  Negative sign 
B)  Positive sign

Question 20

Write the expression in terms of sines and/or cosines, and then simplify.
-

Accepted Answer

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

Find the exact value using a double-angle identity. -sin(480°)

Prove the identity. -

Use identities to find the exact value of the trigonometric function. -Find sec given that sin is in quadrant II.

Find the exact value using a double-angle identity. -cos

Find the exact value by using a half-angle identity. -cos 75°

Show that the equation is not an identity by listing the value(s) of the variable from among for which the equation is false. -sin + cos = tan

Use a sum or difference identity to find the exact value. -sin

Use a product-to-sum identity to rewrite the expression. -

Use a sum-to-product identity to rewrite the expression. -sin 43° + sin 55°

Use an identity to write the expression as a single trigonometric function or as a single number. -

Use identities to find the exact value of the trigonometric function. -Find sin if tan

Identify the equation as either an identity or not. - = (csc x - 1)(csc x + 1)

Identify the equation as either an identity or not. -sin = sin A

Prove that the equation is an identity. -tan x csc x = csc x

Prove that the equation is an identity. -

Show that the equation is not an identity by listing the value(s) of the variable from among for which the equation is false. -

Prove that the equation is an identity. -

Determine whether the positive or negative sign makes the equation correct. -tan

Write the expression in terms of sines and/or cosines, and then simplify. -

Equations, Inequalities, and Modeling

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Exam 6: Trigonometric Identities and Conditional Equations

Find the exact value using a double-angle identity. -sin(480°)

Prove the identity. -

Use identities to find the exact value of the trigonometric function. -Find sec given that sin is in quadrant II.

Find the exact value using a double-angle identity. -cos

Find the exact value by using a half-angle identity. -cos 75°

Show that the equation is not an identity by listing the value(s) of the variable from among for which the equation is false. -sin + cos = tan

Use a sum or difference identity to find the exact value. -sin

Use a product-to-sum identity to rewrite the expression. -

Use a sum-to-product identity to rewrite the expression. -sin 43° + sin 55°

Use an identity to write the expression as a single trigonometric function or as a single number. -

Use identities to find the exact value of the trigonometric function. -Find sin if tan

Identify the equation as either an identity or not. - = (csc x - 1)(csc x + 1)

Identify the equation as either an identity or not. -sin = sin A

Prove that the equation is an identity. -tan x csc x = csc x

Prove that the equation is an identity. -

Show that the equation is not an identity by listing the value(s) of the variable from among for which the equation is false. -

Prove that the equation is an identity. -

Determine whether the positive or negative sign makes the equation correct. -tan

Write the expression in terms of sines and/or cosines, and then simplify. -

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