Question 1

Evaluate the given expression. cos $\frac { \pi } { 2 }$

Accepted Answer

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

Question 2

A manufacturer will supply x units of a certain commodity to the market when the price is $p = S ( x )$ dollars per unit,where $S ( x ) = 23 + 3 x - 2.5 \sin \pi x$ . What is the producers' surplus when x = 5 units?

Accepted Answer

A) $39.09 
B) $113.70 
C) $30.18 
D) $37.50 
A) $39.09 
B) $113.70 
C) $30.18 
D) $37.50 C

Question 3

Specify the number of degrees in the indicated angle. $$\infty$$

Accepted Answer

A)  $150 ^ { \circ }$ 
B)  $210 ^ { \circ }$ 
C)  $240 ^ { \circ }$ 
D)  $- 150 ^ { \circ }$ 
A)  $150 ^ { \circ }$ 
B)  $210 ^ { \circ }$ 
C)  $240 ^ { \circ }$ 
D)  $- 150 ^ { \circ }$ B

Question 4

Solve the given differential equation subject to the specified initial condition. $\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3$

Accepted Answer

A)  $y ( t ) = 3 - \sqrt { \frac { 2 } { 9 } \sin t }$ 
B)  $y ( t ) = 3 + \sqrt { \frac { 2 } { 9 } \sin t }$ 
C)  $y ( t ) = \sqrt { \frac { 2 } { 9 } \sin t + 9 }$ 
D)  $y ( t ) = \sqrt { 9 - \frac { 2 } { 9 } \sin t }$ 
A)  $y ( t ) = 3 - \sqrt { \frac { 2 } { 9 } \sin t }$ 
B)  $y ( t ) = 3 + \sqrt { \frac { 2 } { 9 } \sin t }$ 
C)  $y ( t ) = \sqrt { \frac { 2 } { 9 } \sin t + 9 }$ 
D)  $y ( t ) = \sqrt { 9 - \frac { 2 } { 9 } \sin t }$

Question 5

Differentiate the given function. $g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }$

Accepted Answer

A)  $50 \sin ^ { 9 } t \cdot \cos t - 60 \sin ^ { 9 } t \cdot \cos t$ 
B)  $- 5 \cos ^ { 10 } t + 6 \cos t ^ { 10 }$ 
C)  $5 \cos ^ { 10 } t - 6 \cos ^ { 10 }$ 
D)  $50 \sin ^ { 9 } t \cdot \cos t - 60 t ^ { 9 } \cos t ^ { 10 }$ 
A)  $50 \sin ^ { 9 } t \cdot \cos t - 60 \sin ^ { 9 } t \cdot \cos t$ 
B)  $- 5 \cos ^ { 10 } t + 6 \cos t ^ { 10 }$ 
C)  $5 \cos ^ { 10 } t - 6 \cos ^ { 10 }$ 
D)  $50 \sin ^ { 9 } t \cdot \cos t - 60 t ^ { 9 } \cos t ^ { 10 }$

Question 6

Differentiate the given function. $f ( t ) = \sin 6 t - \cos 4 t$

Accepted Answer

A)  $6 \sin 6 t - 4 \cos 4 t$ 
B)  $6 \cos 6 t + 4 \sin 4 t$ 
C)  $- 6 \cos 6 t + 4 \sin 4 t$ 
D)  $\cos 6 t - \sin 4 t$ 
A)  $6 \sin 6 t - 4 \cos 4 t$ 
B)  $6 \cos 6 t + 4 \sin 4 t$ 
C)  $- 6 \cos 6 t + 4 \sin 4 t$ 
D)  $\cos 6 t - \sin 4 t$

Question 7

Find the volume of the solid generated by rotating the region R about the x-axis.R is the region bounded by the x-axis, $y = \sec x$ , $x = - \frac { \pi } { 4 }$ ,and $x = \frac { \pi } { 4 }$ .

Accepted Answer

A)  $\frac { 45 \pi } { 2 }$ 
B)  $\frac { 9 \pi } { 2 }$ 
C)  $2 \pi$ 
D)  $9 \pi$ 
A)  $\frac { 45 \pi } { 2 }$ 
B)  $\frac { 9 \pi } { 2 }$ 
C)  $2 \pi$ 
D)  $9 \pi$

Question 8

A projectile is fired from a cannon at ground level at an angle of $24 ^ { \circ }$ with an initial velocity of 54 ft/sec.How far from the cannon does the projectile land? Round your answer to the nearest tenth of a foot. 
Use the following formulas 
$$\begin{array} { l } 
x = \left( v _ { 0 } \cos \theta \right) t \
y = - 16 t ^ { 2 } + \left( v _ { 0 } \sin \theta \right) t + s _ { 0 }
\end{array}$$

Accepted Answer

A)   33.9 ft 
B)   37.1 ft 
C)   67.7 ft 
D)   135.4 ft 
A)   33.9 ft 
B)   37.1 ft 
C)   67.7 ft 
D)   135.4 ft

Question 9

Determine the period p,the amplitude b,the phase shift d,and the vertical shift a of the given trigonometric function f(t). $f ( t ) = 2 + 5 \cos \left[ \frac { \pi } { 3 } ( t + 1 ) \right]$

Accepted Answer

A)  $p = 3 , b = - 5 , d = 1 , a = 2$ 
B)  $p = 6 , b = 5 , d = - 1 , a = 2$ 
C)  $p = 3 , b = 5 , d = 1 , a = 2$ 
D)  $p = 6 , b = - 5 , d = 1 , a = 2$ 
A)  $p = 3 , b = - 5 , d = 1 , a = 2$ 
B)  $p = 6 , b = 5 , d = - 1 , a = 2$ 
C)  $p = 3 , b = 5 , d = 1 , a = 2$ 
D)  $p = 6 , b = - 5 , d = 1 , a = 2$

Question 10

Find the indicated integral: $\int ( 20 \cos x - 6 \sin x ) d x$

Accepted Answer

A)  $20 \sin x - 6 \cos x + C$ 
B)  $- 20 \sin x + 6 \cos x + C$ 
C)  $20 \sin x + 6 \cos x + C$ 
D)  $- 20 \sin x - 6 \cos x + C$ 
A)  $20 \sin x - 6 \cos x + C$ 
B)  $- 20 \sin x + 6 \cos x + C$ 
C)  $20 \sin x + 6 \cos x + C$ 
D)  $- 20 \sin x - 6 \cos x + C$

Question 11

Find the indicated integral. $\int x ^ { 5 } \sin \left( 3 + x ^ { 6 } \right) d x$

Accepted Answer

A)  $- \frac { x ^ { 6 } } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C$ 
B)  $\frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C$ 
C)  $- \frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C$ 
D)  $\frac { 1 } { 6 } \sin \left( 3 + x ^ { 6 } \right) + C$ 
A)  $- \frac { x ^ { 6 } } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C$ 
B)  $\frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C$ 
C)  $- \frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C$ 
D)  $\frac { 1 } { 6 } \sin \left( 3 + x ^ { 6 } \right) + C$

Question 12

Convert the indicated angle from degrees to radians. $185 ^ { \circ }$

Accepted Answer

A)  $\frac { 37 \pi } { 36 }$ 
B)  $\frac { 37 \pi } { 18 }$ 
C)  $\frac { 37 \pi } { 72 }$ 
D) None of the above 
A)  $\frac { 37 \pi } { 36 }$ 
B)  $\frac { 37 \pi } { 18 }$ 
C)  $\frac { 37 \pi } { 72 }$ 
D) None of the above

Question 13

Find all values of $\theta$ in the specified interval that satisfy the given equation. $\sin \theta = \cos 2 \theta , 0 \leq \theta \leq 2 \pi$

Accepted Answer

A)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }$ 
B)  $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$ 
C)  $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 }$ 
D)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
A)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }$ 
B)  $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }$ 
C)  $\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 }$ 
D)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$

Question 14

Evaluate the given expression. tan $\frac { 9 \pi } { 4 }$

Accepted Answer

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

Question 15

Convert the indicated angle from radians to degrees. $\frac { 23 \pi } { 12 }$

Accepted Answer

A)  $172.5 ^ { \circ }$ 
B)  $690 ^ { \circ }$ 
C)  $345 ^ { \circ }$ 
D) None of the above 
A)  $172.5 ^ { \circ }$ 
B)  $690 ^ { \circ }$ 
C)  $345 ^ { \circ }$ 
D) None of the above

Question 16

Suppose a company determines that the profit P (in hundreds of dollars)obtained from sales during week t (for $0 \leq t \leq 52$ )of a particular year may be modeled by the trigonometric function $P ( t ) = 115 - 40 \cos \left[ \frac { \pi ( t - 17 ) } { 26 } \right]$ What is the largest weekly profit?

Accepted Answer

A) $15,500 
B) $23,000 
C) $11,500 
D) $7,500 
A) $15,500 
B) $23,000 
C) $11,500 
D) $7,500

Question 17

Find $\sec \theta$ if $\sin \theta = \frac { 3 } { 5 }$

Accepted Answer

A)  $\frac { 5 } { 4 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 4 } { 3 }$ 
A)  $\frac { 5 } { 4 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 4 } { 3 }$

Question 18

Using a graphing utility,find the value of t for which the smallest value of x(t)occurs for the indicated interval.Estimate to four decimal places,if necessary. $x ( t ) = e ^ { - t } ( 4 \sin 3 t + 3 \cos 2 t ) \text { for } 0 \leq t \leq \pi$

Accepted Answer

A)  $t \approx 0.9605$ 
B)  t=0 
C)  $t \approx 0.2632$ 
D) None of the above 
A)  $t \approx 0.9605$ 
B)  t=0 
C)  $t \approx 0.2632$ 
D) None of the above

Question 19

Evaluate the given expression. sec $\left( - \frac { 17 \pi } { 4 } \right)$

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  $- \sqrt { 2 }$ 
D)  $- \frac { \sqrt { 2 } } { 2 }$ 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  $- \sqrt { 2 }$ 
D)  $- \frac { \sqrt { 2 } } { 2 }$

Evaluate the given expression. cos $\frac { \pi } { 2 }$

A manufacturer will supply x units of a certain commodity to the market when the price is $p = S ( x )$ dollars per unit,where $S ( x ) = 23 + 3 x - 2.5 \sin \pi x$ . What is the producers' surplus when x = 5 units?

Specify the number of degrees in the indicated angle. $\infty$

Solve the given differential equation subject to the specified initial condition. $\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3$

Differentiate the given function. $g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }$

Differentiate the given function. $f ( t ) = \sin 6 t - \cos 4 t$

Find the volume of the solid generated by rotating the region R about the x-axis.R is the region bounded by the x-axis, $y = \sec x$ , $x = - \frac { \pi } { 4 }$ ,and $x = \frac { \pi } { 4 }$ .

A projectile is fired from a cannon at ground level at an angle of $24 ^ { \circ }$ with an initial velocity of 54 ft/sec.How far from the cannon does the projectile land? Round your answer to the nearest tenth of a foot. Use the following formulas x= \theta t y=-16+ \theta t+

Determine the period p,the amplitude b,the phase shift d,and the vertical shift a of the given trigonometric function f(t). $f ( t ) = 2 + 5 \cos \left[ \frac { \pi } { 3 } ( t + 1 ) \right]$

Find the indicated integral: $\int ( 20 \cos x - 6 \sin x ) d x$

Find the indicated integral. $\int x ^ { 5 } \sin \left( 3 + x ^ { 6 } \right) d x$

Convert the indicated angle from degrees to radians. $185 ^ { \circ }$

Find all values of $\theta$ in the specified interval that satisfy the given equation. $\sin \theta = \cos 2 \theta , 0 \leq \theta \leq 2 \pi$

Evaluate the given expression. tan $\frac { 9 \pi } { 4 }$

Convert the indicated angle from radians to degrees. $\frac { 23 \pi } { 12 }$

Find $\sec \theta$ if $\sin \theta = \frac { 3 } { 5 }$

Using a graphing utility,find the value of t for which the smallest value of x(t)occurs for the indicated interval.Estimate to four decimal places,if necessary. $x ( t ) = e ^ { - t } ( 4 \sin 3 t + 3 \cos 2 t ) \text { for } 0 \leq t \leq \pi$

Evaluate the given expression. sec $\left( - \frac { 17 \pi } { 4 } \right)$

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Exam 11: Trigonometric Functions

Evaluate the given expression. cos π2\frac { \pi } { 2 }2π​

A manufacturer will supply x units of a certain commodity to the market when the price is p=S(x)p = S ( x )p=S(x) dollars per unit,where S(x)=23+3x−2.5sin⁡πxS ( x ) = 23 + 3 x - 2.5 \sin \pi xS(x)=23+3x−2.5sinπx . What is the producers' surplus when x = 5 units?

Specify the number of degrees in the indicated angle. ∞\infty∞

Solve the given differential equation subject to the specified initial condition. dydt=cos⁡t9y;y(0)=3\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3dtdy​=9ycost​;y(0)=3

Differentiate the given function. g(t)=5sin⁡10t−6sin⁡t10g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }g(t)=5sin10t−6sint10

Differentiate the given function. f(t)=sin⁡6t−cos⁡4tf ( t ) = \sin 6 t - \cos 4 tf(t)=sin6t−cos4t

Find the volume of the solid generated by rotating the region R about the x-axis.R is the region bounded by the x-axis, y=sec⁡xy = \sec xy=secx , x=−π4x = - \frac { \pi } { 4 }x=−4π​ ,and x=π4x = \frac { \pi } { 4 }x=4π​ .

A projectile is fired from a cannon at ground level at an angle of 24∘24 ^ { \circ }24∘ with an initial velocity of 54 ft/sec.How far from the cannon does the projectile land? Round your answer to the nearest tenth of a foot. Use the following formulas x= \theta t y=-16+ \theta t+

Determine the period p,the amplitude b,the phase shift d,and the vertical shift a of the given trigonometric function f(t). f(t)=2+5cos⁡[π3(t+1)]f ( t ) = 2 + 5 \cos \left[ \frac { \pi } { 3 } ( t + 1 ) \right]f(t)=2+5cos[3π​(t+1)]

Find the indicated integral: ∫(20cos⁡x−6sin⁡x)dx\int ( 20 \cos x - 6 \sin x ) d x∫(20cosx−6sinx)dx

Find the indicated integral. ∫x5sin⁡(3+x6)dx\int x ^ { 5 } \sin \left( 3 + x ^ { 6 } \right) d x∫x5sin(3+x6)dx

Convert the indicated angle from degrees to radians. 185∘185 ^ { \circ }185∘

Find all values of θ\thetaθ in the specified interval that satisfy the given equation. sin⁡θ=cos⁡2θ,0≤θ≤2π\sin \theta = \cos 2 \theta , 0 \leq \theta \leq 2 \pisinθ=cos2θ,0≤θ≤2π

Evaluate the given expression. tan 9π4\frac { 9 \pi } { 4 }49π​

Convert the indicated angle from radians to degrees. 23π12\frac { 23 \pi } { 12 }1223π​

Find sec⁡θ\sec \thetasecθ if sin⁡θ=35\sin \theta = \frac { 3 } { 5 }sinθ=53​

Evaluate the given expression. sec (−17π4)\left( - \frac { 17 \pi } { 4 } \right)(−417π​)

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Evaluate the given expression. cos $\frac { \pi } { 2 }$

A manufacturer will supply x units of a certain commodity to the market when the price is $p = S ( x )$ dollars per unit,where $S ( x ) = 23 + 3 x - 2.5 \sin \pi x$ . What is the producers' surplus when x = 5 units?

Specify the number of degrees in the indicated angle. $\infty$

Solve the given differential equation subject to the specified initial condition. $\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3$

Differentiate the given function. $g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }$

Differentiate the given function. $f ( t ) = \sin 6 t - \cos 4 t$

Find the volume of the solid generated by rotating the region R about the x-axis.R is the region bounded by the x-axis, $y = \sec x$ , $x = - \frac { \pi } { 4 }$ ,and $x = \frac { \pi } { 4 }$ .

A projectile is fired from a cannon at ground level at an angle of $24 ^ { \circ }$ with an initial velocity of 54 ft/sec.How far from the cannon does the projectile land? Round your answer to the nearest tenth of a foot. Use the following formulas x= \theta t y=-16+ \theta t+

Determine the period p,the amplitude b,the phase shift d,and the vertical shift a of the given trigonometric function f(t). $f ( t ) = 2 + 5 \cos \left[ \frac { \pi } { 3 } ( t + 1 ) \right]$

Find the indicated integral: $\int ( 20 \cos x - 6 \sin x ) d x$

Find the indicated integral. $\int x ^ { 5 } \sin \left( 3 + x ^ { 6 } \right) d x$

Convert the indicated angle from degrees to radians. $185 ^ { \circ }$

Find all values of $\theta$ in the specified interval that satisfy the given equation. $\sin \theta = \cos 2 \theta , 0 \leq \theta \leq 2 \pi$

Evaluate the given expression. tan $\frac { 9 \pi } { 4 }$

Convert the indicated angle from radians to degrees. $\frac { 23 \pi } { 12 }$

Find $\sec \theta$ if $\sin \theta = \frac { 3 } { 5 }$

Evaluate the given expression. sec $\left( - \frac { 17 \pi } { 4 } \right)$