Question 1

Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below.   ​

Accepted Answer

A) ​     ​   ,   ,   
B) ​     ​   ,   ,   
C) ​     ​   ,   ,   
D) ​     ​   ,   ,   
E) ​     ​   ,   ,   
A) ​     ​   ,   ,   
B) ​     ​   ,   ,   
C) ​     ​   ,   ,   
D) ​     ​   ,   ,   
E) ​     ​   ,   ,

Question 2

In which quadrant must the terminal side of θ  lie if sin θ  and cot  θ  are to have the different sign? ​

Accepted Answer

A) IV 
B) II and III 
C) I and IV 
D) I and II 
E) III and IV 
A) IV 
B) II and III 
C) I and IV 
D) I and II 
E) III and IV

Question 3

Use the reciprocal identities for the following problem. If tan  θ = 0 a , ( a ≠ 0) find cot  θ .

Accepted Answer

The answer of Use the reciprocal identities for the following...

Question 4

Use a ratio identity to find tan  θ  if    and   .

Accepted Answer

The answer of Use a ratio identity to find tan ...

Question 5

There is an angle in standard position whose terminal side contains the point   . Find the distance from the origin to this point. ​

Accepted Answer

A)    
B) 33 
C)    
D)    
E) 11 
A)    
B) 33 
C)    
D)    
E) 11

Question 6

Suppose ABC  is a right triangle with C = 90°. If a = 15 and b = 8, find c .

Accepted Answer

The answer of Suppose ABC  is a right triangle with...

Question 7

For this problem, let   , and   , and find tan  θ
​

Accepted Answer

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

Question 8

Find r  if AB = 32 and AD = 40.   ​

Accepted Answer

A) r = 14 
B) r  = 10 
C) r  = 9 
D) r  = 7 
E) r  = 5 
A) r = 14 
B) r  = 10 
C) r  = 9 
D) r  = 7 
E) r  = 5

Question 9

Graph the circle   with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x -coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.

Accepted Answer

The answer of Graph the circle   with your...

Question 10

Find the right part of the identity.   __________ ​

Accepted Answer

A) cos  α 
B) sec  α 
C) sin  α 
D) cot  α 
E) csc  α 
A) cos  α 
B) sec  α 
C) sin  α 
D) cot  α 
E) csc  α

Question 11

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each   ​

Accepted Answer

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

Question 12

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each

Accepted Answer

The answer of Find the remaining side of a 45° -...

Question 13

The object shown in the figure is a cube (all edges are equal in length).   Suppose the length of diagonal CF  in the figure is   feet. What is the length of edge  AC ? ​

Accepted Answer

A) 5 inches 
B)     inches 
C)     inches 
D)     inches 
E)     inches 
A) 5 inches 
B)     inches 
C)     inches 
D)     inches 
E)     inches

Question 14

Find y if the point (7, y )is on the terminal side of θ  and

Accepted Answer

The answer of Find y if the point (7, y...

Question 15

For this problem, recall that    means   . If   , find   . ​

Accepted Answer

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

Question 16

Find the right part of the identity.   __________ ​

Accepted Answer

A) cot  β 
B) csc  β 
C) tan  β 
D) cos  β 
E) sin  β 
A) cot  β 
B) csc  β 
C) tan  β 
D) cos  β 
E) sin  β

Question 17

Show that the following statement is true by transforming the left side into the right side.

Accepted Answer

We begin by writing everything on the le

Question 18

Find an angle θ  in the fourth quadrant for which tan  θ = - 1 . Look for an angle between 0° and 360°. ​

Accepted Answer

A) 300° 
B) 225° 
C) 120° 
D) 330° 
E) 315° 
A) 300° 
B) 225° 
C) 120° 
D) 330° 
E) 315°

Question 19

Multiply.   ​

Accepted Answer

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

Question 20

Give the reciprocal of the given number.

Accepted Answer

The answer of Give the reciprocal of the given number....

Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below.

In which quadrant must the terminal side of θ lie if sin θ and cot θ are to have the different sign?

Use the reciprocal identities for the following problem. If tan θ = 0 a , ( a ≠ 0) find cot θ .

Use a ratio identity to find tan θ if and .

There is an angle in standard position whose terminal side contains the point . Find the distance from the origin to this point.

Suppose ABC is a right triangle with C = 90°. If a = 15 and b = 8, find c .

For this problem, let , and , and find tan θ

Find r if AB = 32 and AD = 40.

Find the right part of the identity. __________

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each

The object shown in the figure is a cube (all edges are equal in length). Suppose the length of diagonal CF in the figure is feet. What is the length of edge AC ?

Find y if the point (7, y )is on the terminal side of θ and

For this problem, recall that means . If , find .

Find the right part of the identity. __________

Show that the following statement is true by transforming the left side into the right side.

Find an angle θ in the fourth quadrant for which tan θ = - 1 . Look for an angle between 0° and 360°.

Multiply.

Give the reciprocal of the given number.

Right Triangle Trigonometry

Radian Measure

Graphing and Inverse Functions

Identities and Formulas

Equations

Triangles

Complex Numbers and Polar Coordinates

Filters

Exam 1: The Six Trigonometric Functions

Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below. ​

In which quadrant must the terminal side of θ lie if sin θ and cot θ are to have the different sign? ​

Use the reciprocal identities for the following problem. If tan θ = 0 a , ( a ≠ 0) find cot θ .

Use a ratio identity to find tan θ if and .

There is an angle in standard position whose terminal side contains the point . Find the distance from the origin to this point. ​

Suppose ABC is a right triangle with C = 90°. If a = 15 and b = 8, find c .

For this problem, let , and , and find tan θ ​

Find r if AB = 32 and AD = 40. ​

Find the right part of the identity. __________ ​

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each ​

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each

The object shown in the figure is a cube (all edges are equal in length). Suppose the length of diagonal CF in the figure is feet. What is the length of edge AC ? ​

Find y if the point (7, y )is on the terminal side of θ and

For this problem, recall that means . If , find . ​

Find the right part of the identity. __________ ​

Show that the following statement is true by transforming the left side into the right side.

Find an angle θ in the fourth quadrant for which tan θ = - 1 . Look for an angle between 0° and 360°. ​

Multiply. ​

Give the reciprocal of the given number.

Right Triangle Trigonometry

Radian Measure

Graphing and Inverse Functions

Identities and Formulas

Equations

Triangles

Complex Numbers and Polar Coordinates

Filters

Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below.

In which quadrant must the terminal side of θ lie if sin θ and cot θ are to have the different sign?

There is an angle in standard position whose terminal side contains the point . Find the distance from the origin to this point.

For this problem, let , and , and find tan θ

Find r if AB = 32 and AD = 40.

Find the right part of the identity. __________

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each

The object shown in the figure is a cube (all edges are equal in length). Suppose the length of diagonal CF in the figure is feet. What is the length of edge AC ?

For this problem, recall that means . If , find .

Find the right part of the identity. __________

Find an angle θ in the fourth quadrant for which tan θ = - 1 . Look for an angle between 0° and 360°.

Multiply.