Question 1

Find the indefinite integral. 
-Evaluate: $\int _ { 0 } ^ { \pi / 2 } \sin x d x$ Enter just an integer.

Accepted Answer

1

Question 2

Give the values of sin t and cos t, where t is the radian measure of the angle shown.   Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

Accepted Answer

$\frac { \sqrt { 2 } } { 2 }$ , $\frac { \sqrt { 2 } } { 2 }$

Question 3

f(x) = ln( $e ^ { x }$ ∙ tan 2x)Enter your answer without parentheses or labels, no multiplication dot.

Accepted Answer

1 + 2 csc 2x sec 2x

Question 4

Find the indefinite integral. 
-$\int \cos ( \pi - 3 x )$ dx

Accepted Answer

A)  $\frac { 1 } { 3 }$ sin (π - 3x) + C 
B)  - $\frac { 1 } { 3 }$ sin (π - 3x) + C 
C)  3 cos (π- 3x) + C 
D)  -sin (π - 3x) + C 
E)  none of these 
A)  $\frac { 1 } { 3 }$ sin (π - 3x) + C 
B)  - $\frac { 1 } { 3 }$ sin (π - 3x) + C 
C)  3 cos (π- 3x) + C 
D)  -sin (π - 3x) + C 
E)  none of these

Question 5

f(t) = tan $t6$ Enter your answer without parentheses, no labels.

Accepted Answer

The answer of f(t) = tan $t6$ Enter your answer...

Question 6

A river is 600 m wide. A boat enters the water and is pushed by the current at an angle of 30° to its original position. How far downstream from its original position will the boat land?   Enter your answer in the reduced form a $\sqrt { b }$ (no units).

Accepted Answer

The answer of A river is 600 m wide. A...

Question 7

Differentiate.
-cos 2t cos 3t

Accepted Answer

A)  -sin 2t cos 3t - cos 2t sin 3t 
B)  2sin 2t cos 3t + 3cos 2t sin 3t 
C)  -2sin 2t cos 3t - 3cos 2t sin 3t 
D)  none of these 
A)  -sin 2t cos 3t - cos 2t sin 3t 
B)  2sin 2t cos 3t + 3cos 2t sin 3t 
C)  -2sin 2t cos 3t - 3cos 2t sin 3t 
D)  none of these

Question 8

Convert the given angle to degree measure.
--3π

Accepted Answer

The answer of Convert the given angle to degree measure.
--3π...

Question 9

Find the equation of the tangent line to the graph of f(x) = tan x at $\left( \frac { \pi } { 4 } , 1 \right)$ .

Accepted Answer

A)  y = 2x + 1 - $\frac { \pi } { 2 }$ 
B)  y = 2x - $\frac { \pi } { 2 }$ 
C)  y = 2x - 1 
D)  y = 2x + $\frac { \pi } { 2 }$ 
E)  none of these 
A)  y = 2x + 1 - $\frac { \pi } { 2 }$ 
B)  y = 2x - $\frac { \pi } { 2 }$ 
C)  y = 2x - 1 
D)  y = 2x + $\frac { \pi } { 2 }$ 
E)  none of these

Question 10

$\mathrm { e } ^ { \sin ( \cos \mathrm { t } ) }$ Enter cosine before sine (except in the given exponential) and use parentheses around arguments.

Accepted Answer

- @#IMG-DLM& cos(cos

Question 11

ln(1 + sin x)Enter a quotient of sine and cosine functions without parentheses around their arguments.

Accepted Answer

The answer of ln(1 + sin x)Enter a quotient of...

Question 12

Find the indefinite integral. 
-$\int \sin 4 t d t$ Enter your answer without parentheses around the argument of the function.

Accepted Answer

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

Question 13

Convert -150° to radian measure.

Accepted Answer

A)  $\frac { 7 } { 6 }$ 
B)  $\frac { 5 } { 3 }$ 
C)  - $\frac { 5 } { 6 }$ π 
D)  - $\frac { 5 } { 3 }$ π 
E)  none of these 
A)  $\frac { 7 } { 6 }$ 
B)  $\frac { 5 } { 3 }$ 
C)  - $\frac { 5 } { 6 }$ π 
D)  - $\frac { 5 } { 3 }$ π 
E)  none of these

Question 14

Differentiate.
-sin 3x
No parentheses around arguments.

Accepted Answer

The answer of Differentiate.
-sin 3x
No parentheses around arguments....

Question 15

Give the values of sin t and cos t, where t is the radian measure of the angle shown.   Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

Accepted Answer

The answer of Give the values of sin t and...

Question 16

Give the values of tan t and sec t where t is the radian measure of the angle shown.   Enter just $a , b$ where a represents tan t and b represents sec t, fractions and quotients reduced of form $\frac { \mathrm { c } } { \mathrm { d } }$ or $\frac { \sqrt { f } } { g }$ (no labels and no approximations).

Accepted Answer

The answer of Give the values of tan t and...

Question 17

$e ^ { x ^ { 3 } }$ sin $x ^ { 3 }$ Enter your answer in the form P(x) $e^{ Q ( x )}$ ∙(sinR(x) ± cosS(x)) where P, Q, R, S are polynomials in x in standard form. No parentheses around the arguments of sine and cosine.

Accepted Answer

3 @#IMG-DLM& @#IMG-DLM& ∙ (sin

Question 18

Find t such that - $\frac { \pi } { 2 }$ ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = sin $\left( \frac { 3 \pi } { 4 } \right)$ .

Accepted Answer

A)  $\frac { \pi } { 2 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $\frac { \pi } { 6 }$ 
D)  - $\frac { \pi } { 3 }$ 
E)  none of these 
A)  $\frac { \pi } { 2 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $\frac { \pi } { 6 }$ 
D)  - $\frac { \pi } { 3 }$ 
E)  none of these

Question 19

Find the slope of the tangent line to the graph of y = $\mathrm { e } ^ { \tan x }$ at x = 0.
Enter just an integer.

Accepted Answer

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

Question 20

Differentiate.
-sin 3 $x ^ { 2 }$ Do not enter parentheses around arguments.

Accepted Answer

The answer of Differentiate.
-sin 3 $x ^ { 2 }$...

Find the indefinite integral. -Evaluate: $\int _ { 0 } ^ { \pi / 2 } \sin x d x$ Enter just an integer.

Give the values of sin t and cos t, where t is the radian measure of the angle shown. Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

f(x) = ln( $e ^ { x }$ ∙ tan 2x)Enter your answer without parentheses or labels, no multiplication dot.

Find the indefinite integral. - $\int \cos ( \pi - 3 x )$ dx

f(t) = tan $t6$ Enter your answer without parentheses, no labels.

Differentiate. -cos 2t cos 3t

Convert the given angle to degree measure. --3π

Find the equation of the tangent line to the graph of f(x) = tan x at $\left( \frac { \pi } { 4 } , 1 \right)$ .

$\mathrm { e } ^ { \sin ( \cos \mathrm { t } ) }$ Enter cosine before sine (except in the given exponential) and use parentheses around arguments.

ln(1 + sin x)Enter a quotient of sine and cosine functions without parentheses around their arguments.

Find the indefinite integral. - $\int \sin 4 t d t$ Enter your answer without parentheses around the argument of the function.

Convert -150° to radian measure.

Differentiate. -sin 3x No parentheses around arguments.

Give the values of sin t and cos t, where t is the radian measure of the angle shown. Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

$e ^ { x ^ { 3 } }$ sin $x ^ { 3 }$ Enter your answer in the form P(x) $e^{ Q ( x )}$ ∙(sinR(x) ± cosS(x)) where P, Q, R, S are polynomials in x in standard form. No parentheses around the arguments of sine and cosine.

Find t such that - $\frac { \pi } { 2 }$ ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = sin $\left( \frac { 3 \pi } { 4 } \right)$ .

Find the slope of the tangent line to the graph of y = $\mathrm { e } ^ { \tan x }$ at x = 0. Enter just an integer.

Differentiate. -sin 3 $x ^ { 2 }$ Do not enter parentheses around arguments.

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

Find the indefinite integral. -Evaluate: ∫0π/2sin⁡xdx\int _ { 0 } ^ { \pi / 2 } \sin x d x∫0π/2​sinxdx Enter just an integer.

Give the values of sin t and cos t, where t is the radian measure of the angle shown. Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

f(x) = ln( exe ^ { x }ex ∙ tan 2x)Enter your answer without parentheses or labels, no multiplication dot.

Find the indefinite integral. - ∫cos⁡(π−3x)\int \cos ( \pi - 3 x )∫cos(π−3x) dx

f(t) = tan t6t6t6 Enter your answer without parentheses, no labels.

A river is 600 m wide. A boat enters the water and is pushed by the current at an angle of 30° to its original position. How far downstream from its original position will the boat land? Enter your answer in the reduced form a b\sqrt { b }b​ (no units).

Differentiate. -cos 2t cos 3t

Convert the given angle to degree measure. --3π

Find the equation of the tangent line to the graph of f(x) = tan x at (π4,1)\left( \frac { \pi } { 4 } , 1 \right)(4π​,1) .

esin⁡(cos⁡t)\mathrm { e } ^ { \sin ( \cos \mathrm { t } ) }esin(cost) Enter cosine before sine (except in the given exponential) and use parentheses around arguments.

ln(1 + sin x)Enter a quotient of sine and cosine functions without parentheses around their arguments.

Find the indefinite integral. - ∫sin⁡4tdt\int \sin 4 t d t∫sin4tdt Enter your answer without parentheses around the argument of the function.

Convert -150° to radian measure.

Differentiate. -sin 3x No parentheses around arguments.

Give the values of sin t and cos t, where t is the radian measure of the angle shown. Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

ex3e ^ { x ^ { 3 } }ex3 sin x3x ^ { 3 }x3 Enter your answer in the form P(x) eQ(x)e^{ Q ( x )}eQ(x) ∙(sinR(x) ± cosS(x)) where P, Q, R, S are polynomials in x in standard form. No parentheses around the arguments of sine and cosine.

Find t such that - π2\frac { \pi } { 2 }2π​ ≤ t ≤ π2\frac { \pi } { 2 }2π​ and sin t = sin (3π4)\left( \frac { 3 \pi } { 4 } \right)(43π​) .

Find the slope of the tangent line to the graph of y = etan⁡x\mathrm { e } ^ { \tan x }etanx at x = 0. Enter just an integer.

Differentiate. -sin 3 x2x ^ { 2 }x2 Do not enter parentheses around arguments.

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

Find the indefinite integral. -Evaluate: $\int _ { 0 } ^ { \pi / 2 } \sin x d x$ Enter just an integer.

f(x) = ln( $e ^ { x }$ ∙ tan 2x)Enter your answer without parentheses or labels, no multiplication dot.

Find the indefinite integral. - $\int \cos ( \pi - 3 x )$ dx

f(t) = tan $t6$ Enter your answer without parentheses, no labels.

Find the equation of the tangent line to the graph of f(x) = tan x at $\left( \frac { \pi } { 4 } , 1 \right)$ .

$\mathrm { e } ^ { \sin ( \cos \mathrm { t } ) }$ Enter cosine before sine (except in the given exponential) and use parentheses around arguments.

Find the indefinite integral. - $\int \sin 4 t d t$ Enter your answer without parentheses around the argument of the function.

$e ^ { x ^ { 3 } }$ sin $x ^ { 3 }$ Enter your answer in the form P(x) $e^{ Q ( x )}$ ∙(sinR(x) ± cosS(x)) where P, Q, R, S are polynomials in x in standard form. No parentheses around the arguments of sine and cosine.

Find t such that - $\frac { \pi } { 2 }$ ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = sin $\left( \frac { 3 \pi } { 4 } \right)$ .

Find the slope of the tangent line to the graph of y = $\mathrm { e } ^ { \tan x }$ at x = 0. Enter just an integer.

Differentiate. -sin 3 $x ^ { 2 }$ Do not enter parentheses around arguments.