Question 1

$$\cos ^ { 2 }$$ (x + 4)
Enter cosines before sines with parentheses around arguments.

Accepted Answer

-2 cos(x +

Question 2

Convert the given angle to degree measure.
-- $\frac { 3 \pi } { 15 }$

Accepted Answer

The answer of Convert the given angle to degree measure.
--...

Question 3

Find the indefinite integral. 
-$\int \sin t \cos t d t$ Enter your answer in terms of cosine without using parentheses.

Accepted Answer

The answer of Find the indefinite integral. 
-\(\int \sin t...

Question 4

Does this represent an angle of - $\frac { 3 \pi } { 4 }$ radians?

Accepted Answer

A) True 
 B)False

Question 5

Suppose in a study of a prarie dog town it is discovered that the number of prarie dogs at any time t is given by $\mathrm { P } ( \mathrm { t } ) = 1000 + 500 \cos \left( \frac { 2 \pi \mathrm { t } } { 12 } \right)$ , where t is measured in months from July 1, 1990. What is the average number of prarie dogs living in the town from July 1, 1990 to July 1, 1992?
Enter just an integer.

Accepted Answer

The answer of Suppose in a study of a prarie...

Question 6

Determine the value of sin t when t = $\frac { 11 \pi } { 2 }$ .

Accepted Answer

A)  1 
B)  $\frac { 1 } { 2 }$ 
C)  -1 
D)  0 
E)  none of these 
A)  1 
B)  $\frac { 1 } { 2 }$ 
C)  -1 
D)  0 
E)  none of these

Question 7

Give the value of sin t where t is the radian measure of the angle shown.

Accepted Answer

A)  $\frac { 2 } { \sqrt { 8 } }$ = $\frac { \sqrt { 2 } } { 2 }$ 
B)  2 
C)  - $\frac { 2 } { 2 }$ = -1 
D)  -2 
E)  none of these 
A)  $\frac { 2 } { \sqrt { 8 } }$ = $\frac { \sqrt { 2 } } { 2 }$ 
B)  2 
C)  - $\frac { 2 } { 2 }$ = -1 
D)  -2 
E)  none of these

Question 8

f(x) = $\frac { \sin x ^ { 2 } } { \tan x }$ Enter a quotient with cosine and sine functions last in their terms. No parentheses or labels or multiplication dots.

Accepted Answer

The answer of f(x) = \(\frac { \sin x ^...

Question 9

Which of the following angles could represent the angle - $\frac { 17 \pi } { 12 }$ ?

Accepted Answer

A)    
B)    
C)    
D)  none of these 
A)    
B)    
C)    
D)  none of these

Question 10

A person's blood pressure P at time t is given by P(t) = 90 + 30 sin $\frac { 7 \pi t } { 3 }$ , where t is measured in seconds. What is the average blood pressure over a time interval of 60 seconds?
Enter just an integer (no units).

Accepted Answer

The answer of A person's blood pressure P at time...

Question 11

In a large city, the amount of sulfur dioxide pollutant released into the atmosphere due to the burning of coal and oil for heating purposes is given approximately by $P ( t ) = 3 + \cos \frac { \pi t } { 26 }$ for $0 \leq \mathrm { t } \leq 104$ where P(t) is the amount of sulfur dioxide in tons released during the nth week after January 1. How many tons (to the nearest ton) of pollutants were emitted into the atmosphere from t = 0 to t = 65?

Accepted Answer

A)  221 tons 
B)  4 tons 
C)  196 tons 
D)  203 tons 
A)  221 tons 
B)  4 tons 
C)  196 tons 
D)  203 tons

Question 12

Find t such that 0 ≤ t ≤ π and cos t = cos $\left( - \frac { 2 \pi } { 3 } \right)$ .
Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

Accepted Answer

The answer of Find t such that 0 ≤ t...

Question 13

$\int \csc ^ { 2 } ( 3 x + 1 )$ dx
Enter your answer using parentheses around the argument of the function.

Accepted Answer

The answer of \(\int \csc ^ { 2 } (...

Question 14

Find the indefinite integral. 
-$\int 4 \sin 2 t d t$ Enter your answer without parentheses.

Accepted Answer

The answer of Find the indefinite integral. 
-\(\int 4 \sin...

Question 15

Find the indefinite integral. 
-$\int 3 \sin ( t - \pi ) d t$

Accepted Answer

A)  3 cos(t - π) + C 
B)  -3 cos t + C 
C)  -3 cos(t - π) + C 
D)  3π cos(t - π) + C 
E)  none of these 
A)  3 cos(t - π) + C 
B)  -3 cos t + C 
C)  -3 cos(t - π) + C 
D)  3π cos(t - π) + C 
E)  none of these

Question 16

Find t such that - $\frac { \pi } { 2 }$ ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = sin $\left( \frac { 10 \pi } { 3 } \right)$ .
Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

Accepted Answer

The answer of Find t such that - \(\frac {...

Question 17

Find the slope of the line tangent to the graph of y = sin 2t at t = $\frac { \pi } { 3 }$ .
Enter just an integer.

Accepted Answer

The answer of Find the slope of the line tangent...

Question 18

Differentiate.
-$e ^ { x ^ { 3 } }$ sin $x ^ { 3 }$

Accepted Answer

A)  3x( $e ^ { x ^ { 3 } }$ + cos $x ^ { 3 }$ ) 
B)  $e ^ { x ^ { 3 } }$ (sin $x ^ { 3 }$ + cos $x ^ { 3 }$ ) 
C)  3 $x ^ { 2 }$ ( $e ^ { x ^ { 3 } }$ + cos $x ^ { 3 }$ ) 
D)  3 $x ^ { 2 }$ $e ^ { x ^ { 3 } }$ (sin $x ^ { 3 }$ + cos $x ^ { 3 }$ ) 
A)  3x( $e ^ { x ^ { 3 } }$ + cos $x ^ { 3 }$ ) 
B)  $e ^ { x ^ { 3 } }$ (sin $x ^ { 3 }$ + cos $x ^ { 3 }$ ) 
C)  3 $x ^ { 2 }$ ( $e ^ { x ^ { 3 } }$ + cos $x ^ { 3 }$ ) 
D)  3 $x ^ { 2 }$ $e ^ { x ^ { 3 } }$ (sin $x ^ { 3 }$ + cos $x ^ { 3 }$ )

Question 19

sin x cos 3x
Enter cosine terms first, no parentheses around arguments.

Accepted Answer

cos x cos

Question 20

Find t such that 0 ≤ t ≤ π and cos t = cos $\left( - \frac { 7 \pi } { 6 } \right)$ .
Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

Accepted Answer

The answer of Find t such that 0 ≤ t...

$\cos ^ { 2 }$ (x + 4) Enter cosines before sines with parentheses around arguments.

Convert the given angle to degree measure. -- $\frac { 3 \pi } { 15 }$

Find the indefinite integral. - $\int \sin t \cos t d t$ Enter your answer in terms of cosine without using parentheses.

Does this represent an angle of - $\frac { 3 \pi } { 4 }$ radians? $Does this represent an angle of - \frac { 3 \pi } { 4 } radians?$

Determine the value of sin t when t = $\frac { 11 \pi } { 2 }$ .

Give the value of sin t where t is the radian measure of the angle shown.

f(x) = $\frac { \sin x ^ { 2 } } { \tan x }$ Enter a quotient with cosine and sine functions last in their terms. No parentheses or labels or multiplication dots.

Which of the following angles could represent the angle - $\frac { 17 \pi } { 12 }$ ?

A person's blood pressure P at time t is given by P(t) = 90 + 30 sin $\frac { 7 \pi t } { 3 }$ , where t is measured in seconds. What is the average blood pressure over a time interval of 60 seconds? Enter just an integer (no units).

Find t such that 0 ≤ t ≤ π and cos t = cos $\left( - \frac { 2 \pi } { 3 } \right)$ . Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

$\int \csc ^ { 2 } ( 3 x + 1 )$ dx Enter your answer using parentheses around the argument of the function.

Find the indefinite integral. - $\int 4 \sin 2 t d t$ Enter your answer without parentheses.

Find the indefinite integral. - $\int 3 \sin ( t - \pi ) d t$

Find t such that - $\frac { \pi } { 2 }$ ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = sin $\left( \frac { 10 \pi } { 3 } \right)$ . Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

Find the slope of the line tangent to the graph of y = sin 2t at t = $\frac { \pi } { 3 }$ . Enter just an integer.

Differentiate. - $e ^ { x ^ { 3 } }$ sin $x ^ { 3 }$

sin x cos 3x Enter cosine terms first, no parentheses around arguments.

Find t such that 0 ≤ t ≤ π and cos t = cos $\left( - \frac { 7 \pi } { 6 } \right)$ . Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

The Derivative

Applications of the Derivative

Techniques of Differentiation

Logarithm Functions

Applications of the Exponential and Natural Logarithm Functions

The Definite Integral

Functions of Several Variables

Techniques of Integration

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Filters

Exam 8: The Trigonometric Functions

cos⁡2\cos ^ { 2 }cos2 (x + 4) Enter cosines before sines with parentheses around arguments.

Convert the given angle to degree measure. -- 3π15\frac { 3 \pi } { 15 }153π​

Find the indefinite integral. - ∫sin⁡tcos⁡tdt\int \sin t \cos t d t∫sintcostdt Enter your answer in terms of cosine without using parentheses.

Does this represent an angle of - 3π4\frac { 3 \pi } { 4 }43π​ radians?

Determine the value of sin t when t = 11π2\frac { 11 \pi } { 2 }211π​ .

Give the value of sin t where t is the radian measure of the angle shown.

f(x) = sin⁡x2tan⁡x\frac { \sin x ^ { 2 } } { \tan x }tanxsinx2​ Enter a quotient with cosine and sine functions last in their terms. No parentheses or labels or multiplication dots.

Which of the following angles could represent the angle - 17π12\frac { 17 \pi } { 12 }1217π​ ?

A person's blood pressure P at time t is given by P(t) = 90 + 30 sin 7πt3\frac { 7 \pi t } { 3 }37πt​ , where t is measured in seconds. What is the average blood pressure over a time interval of 60 seconds? Enter just an integer (no units).

Find t such that 0 ≤ t ≤ π and cos t = cos (−2π3)\left( - \frac { 2 \pi } { 3 } \right)(−32π​) . Enter just a reduced quotient of form ab\frac { a } { b }ba​ with π in the numerator (unlabeled).

∫csc⁡2(3x+1)\int \csc ^ { 2 } ( 3 x + 1 )∫csc2(3x+1) dx Enter your answer using parentheses around the argument of the function.

Find the indefinite integral. - ∫4sin⁡2tdt\int 4 \sin 2 t d t∫4sin2tdt Enter your answer without parentheses.

Find the indefinite integral. - ∫3sin⁡(t−π)dt\int 3 \sin ( t - \pi ) d t∫3sin(t−π)dt

Find t such that - π2\frac { \pi } { 2 }2π​ ≤ t ≤ π2\frac { \pi } { 2 }2π​ and sin t = sin (10π3)\left( \frac { 10 \pi } { 3 } \right)(310π​) . Enter just a reduced quotient of form ab\frac { a } { b }ba​ with π in the numerator (unlabeled).

Find the slope of the line tangent to the graph of y = sin 2t at t = π3\frac { \pi } { 3 }3π​ . Enter just an integer.

Differentiate. - ex3e ^ { x ^ { 3 } }ex3 sin x3x ^ { 3 }x3

sin x cos 3x Enter cosine terms first, no parentheses around arguments.

Find t such that 0 ≤ t ≤ π and cos t = cos (−7π6)\left( - \frac { 7 \pi } { 6 } \right)(−67π​) . Enter just a reduced quotient of form ab\frac { a } { b }ba​ with π in the numerator (unlabeled).

The Derivative

Applications of the Derivative

Techniques of Differentiation

Logarithm Functions

Applications of the Exponential and Natural Logarithm Functions

The Definite Integral

Functions of Several Variables

Techniques of Integration

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Filters

$\cos ^ { 2 }$ (x + 4) Enter cosines before sines with parentheses around arguments.

Convert the given angle to degree measure. -- $\frac { 3 \pi } { 15 }$

Find the indefinite integral. - $\int \sin t \cos t d t$ Enter your answer in terms of cosine without using parentheses.

Does this represent an angle of - $\frac { 3 \pi } { 4 }$ radians? $Does this represent an angle of - \frac { 3 \pi } { 4 } radians?$

Determine the value of sin t when t = $\frac { 11 \pi } { 2 }$ .

f(x) = $\frac { \sin x ^ { 2 } } { \tan x }$ Enter a quotient with cosine and sine functions last in their terms. No parentheses or labels or multiplication dots.

Which of the following angles could represent the angle - $\frac { 17 \pi } { 12 }$ ?

A person's blood pressure P at time t is given by P(t) = 90 + 30 sin $\frac { 7 \pi t } { 3 }$ , where t is measured in seconds. What is the average blood pressure over a time interval of 60 seconds? Enter just an integer (no units).

Find t such that 0 ≤ t ≤ π and cos t = cos $\left( - \frac { 2 \pi } { 3 } \right)$ . Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

$\int \csc ^ { 2 } ( 3 x + 1 )$ dx Enter your answer using parentheses around the argument of the function.

Find the indefinite integral. - $\int 4 \sin 2 t d t$ Enter your answer without parentheses.

Find the indefinite integral. - $\int 3 \sin ( t - \pi ) d t$

Find t such that - $\frac { \pi } { 2 }$ ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = sin $\left( \frac { 10 \pi } { 3 } \right)$ . Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).

Find the slope of the line tangent to the graph of y = sin 2t at t = $\frac { \pi } { 3 }$ . Enter just an integer.

Differentiate. - $e ^ { x ^ { 3 } }$ sin $x ^ { 3 }$

Find t such that 0 ≤ t ≤ π and cos t = cos $\left( - \frac { 7 \pi } { 6 } \right)$ . Enter just a reduced quotient of form $\frac { a } { b }$ with π in the numerator (unlabeled).