Question 1

If sin x =
 
And cos x < 0, find sin 2x.

Accepted Answer

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

Question 2

The number of deer on an island is given by
   where x is the number of years since 2000. During what year is it the first time after 2000 that the number of deer reaches 250?

Accepted Answer

2003

Question 3

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Accepted Answer

The answer of Solve the given trigonometric equation exactly over...

Question 4

Use fundamental identities to simplify sec x cot x.

Accepted Answer

A)  sec2 x 
B)  csc2 x 
C)  tan x 
D)  csc x 
A)  sec2 x 
B)  csc2 x 
C)  tan x 
D)  csc x

Question 5

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Accepted Answer

The answer of Solve the given trigonometric equation on 0°...

Question 6

Use fundamental identities to simplify

Accepted Answer

The answer of Use fundamental identities to simplify 
 ...

Question 7

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Accepted Answer

The answer of Solve the given trigonometric equation exactly over...

Question 8

Write cos 1.2x + cos 0.6x as a product of sines and/or cosines.

Accepted Answer

The answer of Write cos 1.2x + cos 0.6x as...

Question 9

Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.

Accepted Answer

The answer of Use a calculator to evaluate the expression....

Question 10

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Accepted Answer

The answer of Solve the given trigonometric equation exactly over...

Question 11

Simplify the trigonometric expression

Accepted Answer

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

Question 12

Area of a Triangle. A formula for finding the area of a triangle when given the measures of the angles and one side is area =
  
where a is the length of the side opposite angle A. If the measures of angles B and C are26° and 61° , respectively, and if a = 19 feet, use the appropriate product-to-sum identity to change the formula so that you can solve for the area of a triangle. Round your answer to two decimal places.

Accepted Answer

A)  69.30 ft2 
B)  3.65 ft2 
C)  138.60 ft2 
D)  69.11 ft2 
A)  69.30 ft2 
B)  3.65 ft2 
C)  138.60 ft2 
D)  69.11 ft2

Question 13

Use a half-angle identity to find tan
   
if csc x =
   
and
   
. Give the exact answer. Do not rationalize the denominator.

Accepted Answer

The answer of Use a half-angle identity to find tan
...

Question 14

Use a half-angle identity to find the exact value of csc 202.5°. Rationalize the denominator once only, if necessary.

Accepted Answer

The answer of Use a half-angle identity to find the...

Question 15

Verify the trigonometric identity 
   
algebraically.

Accepted Answer

The answer of Verify the trigonometric identity 
  ...

Question 16

Write   as a product of sines and/or cosines.

Accepted Answer

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

Question 17

Write sin 3x cos 8x as a sum or difference of sines and/or cosines.

Accepted Answer

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

Question 18

Use a half-angle identity to find the exact value of sec

Accepted Answer

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

Question 19

Assume that light is going from air into a cubic zirconia ring. Calculate the refractive angle θr if the incidence angle is θi = 37°  and the index of refraction values for air and cubic zirconia are ni = 1.00 and nr = 2.16, respectively. Round to the nearest degree. The Snell's law is given as 
   
.

Accepted Answer

Question 20

Evaluate the expression exactly if possible. If not possible, state why.

Accepted Answer

The answer of Evaluate the expression exactly if possible. If...

If sin x = And cos x < 0, find sin 2x.

The number of deer on an island is given by where x is the number of years since 2000. During what year is it the first time after 2000 that the number of deer reaches 250?

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Use fundamental identities to simplify sec x cot x.

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Use fundamental identities to simplify

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Write cos 1.2x + cos 0.6x as a product of sines and/or cosines.

Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Simplify the trigonometric expression

Use a half-angle identity to find tan if csc x = and . Give the exact answer. Do not rationalize the denominator.

Use a half-angle identity to find the exact value of csc 202.5°. Rationalize the denominator once only, if necessary.

Verify the trigonometric identity algebraically.

Write as a product of sines and/or cosines.

Write sin 3x cos 8x as a sum or difference of sines and/or cosines.

Use a half-angle identity to find the exact value of sec

Evaluate the expression exactly if possible. If not possible, state why.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions of Angles

Trigonometric Functions of Real Numbers

Vectors, the Complex Plane, and Polar Coordinates

Systems of Linear Equations and Inequalities

Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

Sequences and Series

Limits: A Preview to Calculus

Review: Equations and Inequalities

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Exam 6: Analytic Trigonometry

If sin x = And cos x < 0, find sin 2x.

The number of deer on an island is given by where x is the number of years since 2000. During what year is it the first time after 2000 that the number of deer reaches 250?

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Use fundamental identities to simplify sec x cot x.

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Use fundamental identities to simplify

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Write cos 1.2x + cos 0.6x as a product of sines and/or cosines.

Use a calculator to evaluate the expression. Give answer in radians and round to two decimal places.

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Simplify the trigonometric expression

Use a half-angle identity to find tan if csc x = and . Give the exact answer. Do not rationalize the denominator.

Use a half-angle identity to find the exact value of csc 202.5°. Rationalize the denominator once only, if necessary.

Verify the trigonometric identity algebraically.

Write as a product of sines and/or cosines.

Write sin 3x cos 8x as a sum or difference of sines and/or cosines.

Use a half-angle identity to find the exact value of sec

Assume that light is going from air into a cubic zirconia ring. Calculate the refractive angle θr if the incidence angle is θi = 37° and the index of refraction values for air and cubic zirconia are ni = 1.00 and nr = 2.16, respectively. Round to the nearest degree. The Snell's law is given as .

Evaluate the expression exactly if possible. If not possible, state why.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions of Angles

Trigonometric Functions of Real Numbers

Vectors, the Complex Plane, and Polar Coordinates

Systems of Linear Equations and Inequalities

Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

Sequences and Series

Limits: A Preview to Calculus

Review: Equations and Inequalities

Filters