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Deck 11: Trigonometric Functions

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

A) 22\frac { \sqrt { 2 } } { 2 }
B) 2\sqrt { 2 }
C) −2- \sqrt { 2 }
D) −22- \frac { \sqrt { 2 } } { 2 }
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Question
Find the indicated integral. ∫x5sin⁡(3+x6)dx\int x ^ { 5 } \sin \left( 3 + x ^ { 6 } \right) d x

A) −x66cos⁡(3+x6)+C- \frac { x ^ { 6 } } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C
B) 16cos⁡(3+x6)+C\frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C
C) −16cos⁡(3+x6)+C- \frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C
D) 16sin⁡(3+x6)+C\frac { 1 } { 6 } \sin \left( 3 + x ^ { 6 } \right) + C
Question
Find all values of θ\theta 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 \pi

A) θ=π6,5π6,3π2\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }
B) θ=π6,π2,5π6\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }
C) θ=π6,π2\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 }
D) θ=π6,5π6\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }
Question
Differentiate the given function. f(t)=sin⁡6t−cos⁡4tf ( t ) = \sin 6 t - \cos 4 t

A) 6sin⁡6t−4cos⁡4t6 \sin 6 t - 4 \cos 4 t
B) 6cos⁡6t+4sin⁡4t6 \cos 6 t + 4 \sin 4 t
C) −6cos⁡6t+4sin⁡4t- 6 \cos 6 t + 4 \sin 4 t
D) cos⁡6t−sin⁡4t\cos 6 t - \sin 4 t
Question
A manufacturer will supply x units of a certain commodity to the market when the price is 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 x . What is the producers' surplus when x = 5 units?

A)$39.09
B)$113.70
C)$30.18
D)$37.50
Question
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 ) = 3

A) y(t)=3−29sin⁡ty ( t ) = 3 - \sqrt { \frac { 2 } { 9 } \sin t }
B) y(t)=3+29sin⁡ty ( t ) = 3 + \sqrt { \frac { 2 } { 9 } \sin t }
C) y(t)=29sin⁡t+9y ( t ) = \sqrt { \frac { 2 } { 9 } \sin t + 9 }
D) y(t)=9−29sin⁡ty ( t ) = \sqrt { 9 - \frac { 2 } { 9 } \sin t }
Question
Find the indicated integral: ∫(20cos⁡x−6sin⁡x)dx\int ( 20 \cos x - 6 \sin x ) d x

A) 20sin⁡x−6cos⁡x+C20 \sin x - 6 \cos x + C
B) −20sin⁡x+6cos⁡x+C- 20 \sin x + 6 \cos x + C
C) 20sin⁡x+6cos⁡x+C20 \sin x + 6 \cos x + C
D) −20sin⁡x−6cos⁡x+C- 20 \sin x - 6 \cos x + C
Question
Convert the indicated angle from degrees to radians. 185∘185 ^ { \circ }

A) 37π36\frac { 37 \pi } { 36 }
B) 37π18\frac { 37 \pi } { 18 }
C) 37π72\frac { 37 \pi } { 72 }
D)None of the above
Question
Differentiate the given function. g(t)=5sin⁡10t−6sin⁡t10g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }

A) 50sin⁡9t⋅cos⁡t−60sin⁡9t⋅cos⁡t50 \sin ^ { 9 } t \cdot \cos t - 60 \sin ^ { 9 } t \cdot \cos t
B) −5cos⁡10t+6cos⁡t10- 5 \cos ^ { 10 } t + 6 \cos t ^ { 10 }
C) 5cos⁡10t−6cos⁡105 \cos ^ { 10 } t - 6 \cos ^ { 10 }
D) 50sin⁡9t⋅cos⁡t−60t9cos⁡t1050 \sin ^ { 9 } t \cdot \cos t - 60 t ^ { 9 } \cos t ^ { 10 }
Question
A projectile is fired from a cannon at ground level at an angle of 24∘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=(v0cos⁡θ)ty=−16t2+(v0sin⁡θ)t+s0\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}

A) 33.9 ft
B) 37.1 ft
C) 67.7 ft
D) 135.4 ft
Question
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 x , x=−π4x = - \frac { \pi } { 4 } ,and x=π4x = \frac { \pi } { 4 } .

A) 45π2\frac { 45 \pi } { 2 }
B) 9π2\frac { 9 \pi } { 2 }
C) 2π2 \pi
D) 9π9 \pi
Question
Find sec⁡θ\sec \theta if sin⁡θ=35\sin \theta = \frac { 3 } { 5 }

A) 54\frac { 5 } { 4 }
B) 45\frac { 4 } { 5 }
C) 34\frac { 3 } { 4 }
D) 43\frac { 4 } { 3 }
Question
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(4sin⁡3t+3cos⁡2t) for 0≤t≤πx ( t ) = e ^ { - t } ( 4 \sin 3 t + 3 \cos 2 t ) \text { for } 0 \leq t \leq \pi

A) t≈0.9605t \approx 0.9605
B) t=0
C) t≈0.2632t \approx 0.2632
D)None of the above
Question
Specify the number of degrees in the indicated angle. ∞\infty

A) 150∘150 ^ { \circ }
B) 210∘210 ^ { \circ }
C) 240∘240 ^ { \circ }
D) −150∘- 150 ^ { \circ }
Question
Convert the indicated angle from radians to degrees. 23π12\frac { 23 \pi } { 12 }

A) 172.5∘172.5 ^ { \circ }
B) 690∘690 ^ { \circ }
C) 345∘345 ^ { \circ }
D)None of the above
Question
Suppose a company determines that the profit P (in hundreds of dollars)obtained from sales during week t (for 0≤t≤520 \leq t \leq 52 )of a particular year may be modeled by the trigonometric function P(t)=115−40cos⁡[π(t−17)26]P ( t ) = 115 - 40 \cos \left[ \frac { \pi ( t - 17 ) } { 26 } \right] What is the largest weekly profit?

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

A) p=3,b=−5,d=1,a=2p = 3 , b = - 5 , d = 1 , a = 2
B) p=6,b=5,d=−1,a=2p = 6 , b = 5 , d = - 1 , a = 2
C) p=3,b=5,d=1,a=2p = 3 , b = 5 , d = 1 , a = 2
D) p=6,b=−5,d=1,a=2p = 6 , b = - 5 , d = 1 , a = 2
Question
Evaluate the given expression. cos π2\frac { \pi } { 2 }

A)Undefined
B)-1
C)0
D)1
Question
Evaluate the given expression. tan 9π4\frac { 9 \pi } { 4 }

A)1
B)0
C)-1
D)undefined
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Deck 11: Trigonometric Functions
1
Evaluate the given expression. sec (−17π4)\left( - \frac { 17 \pi } { 4 } \right)

A) 22\frac { \sqrt { 2 } } { 2 }
B) 2\sqrt { 2 }
C) −2- \sqrt { 2 }
D) −22- \frac { \sqrt { 2 } } { 2 }
2\sqrt { 2 }
2
Find the indicated integral. ∫x5sin⁡(3+x6)dx\int x ^ { 5 } \sin \left( 3 + x ^ { 6 } \right) d x

A) −x66cos⁡(3+x6)+C- \frac { x ^ { 6 } } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C
B) 16cos⁡(3+x6)+C\frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C
C) −16cos⁡(3+x6)+C- \frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C
D) 16sin⁡(3+x6)+C\frac { 1 } { 6 } \sin \left( 3 + x ^ { 6 } \right) + C
−16cos⁡(3+x6)+C- \frac { 1 } { 6 } \cos \left( 3 + x ^ { 6 } \right) + C
3
Find all values of θ\theta 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 \pi

A) θ=π6,5π6,3π2\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }
B) θ=π6,π2,5π6\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 }
C) θ=π6,π2\theta = \frac { \pi } { 6 } , \frac { \pi } { 2 }
D) θ=π6,5π6\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }
θ=π6,5π6,3π2\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }
4
Differentiate the given function. f(t)=sin⁡6t−cos⁡4tf ( t ) = \sin 6 t - \cos 4 t

A) 6sin⁡6t−4cos⁡4t6 \sin 6 t - 4 \cos 4 t
B) 6cos⁡6t+4sin⁡4t6 \cos 6 t + 4 \sin 4 t
C) −6cos⁡6t+4sin⁡4t- 6 \cos 6 t + 4 \sin 4 t
D) cos⁡6t−sin⁡4t\cos 6 t - \sin 4 t
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5
A manufacturer will supply x units of a certain commodity to the market when the price is 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 x . What is the producers' surplus when x = 5 units?

A)$39.09
B)$113.70
C)$30.18
D)$37.50
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6
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 ) = 3

A) y(t)=3−29sin⁡ty ( t ) = 3 - \sqrt { \frac { 2 } { 9 } \sin t }
B) y(t)=3+29sin⁡ty ( t ) = 3 + \sqrt { \frac { 2 } { 9 } \sin t }
C) y(t)=29sin⁡t+9y ( t ) = \sqrt { \frac { 2 } { 9 } \sin t + 9 }
D) y(t)=9−29sin⁡ty ( t ) = \sqrt { 9 - \frac { 2 } { 9 } \sin t }
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7
Find the indicated integral: ∫(20cos⁡x−6sin⁡x)dx\int ( 20 \cos x - 6 \sin x ) d x

A) 20sin⁡x−6cos⁡x+C20 \sin x - 6 \cos x + C
B) −20sin⁡x+6cos⁡x+C- 20 \sin x + 6 \cos x + C
C) 20sin⁡x+6cos⁡x+C20 \sin x + 6 \cos x + C
D) −20sin⁡x−6cos⁡x+C- 20 \sin x - 6 \cos x + C
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8
Convert the indicated angle from degrees to radians. 185∘185 ^ { \circ }

A) 37π36\frac { 37 \pi } { 36 }
B) 37π18\frac { 37 \pi } { 18 }
C) 37π72\frac { 37 \pi } { 72 }
D)None of the above
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9
Differentiate the given function. g(t)=5sin⁡10t−6sin⁡t10g ( t ) = 5 \sin ^ { 10 } t - 6 \sin t ^ { 10 }

A) 50sin⁡9t⋅cos⁡t−60sin⁡9t⋅cos⁡t50 \sin ^ { 9 } t \cdot \cos t - 60 \sin ^ { 9 } t \cdot \cos t
B) −5cos⁡10t+6cos⁡t10- 5 \cos ^ { 10 } t + 6 \cos t ^ { 10 }
C) 5cos⁡10t−6cos⁡105 \cos ^ { 10 } t - 6 \cos ^ { 10 }
D) 50sin⁡9t⋅cos⁡t−60t9cos⁡t1050 \sin ^ { 9 } t \cdot \cos t - 60 t ^ { 9 } \cos t ^ { 10 }
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10
A projectile is fired from a cannon at ground level at an angle of 24∘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=(v0cos⁡θ)ty=−16t2+(v0sin⁡θ)t+s0\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}

A) 33.9 ft
B) 37.1 ft
C) 67.7 ft
D) 135.4 ft
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11
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 x , x=−π4x = - \frac { \pi } { 4 } ,and x=π4x = \frac { \pi } { 4 } .

A) 45π2\frac { 45 \pi } { 2 }
B) 9π2\frac { 9 \pi } { 2 }
C) 2π2 \pi
D) 9π9 \pi
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12
Find sec⁡θ\sec \theta if sin⁡θ=35\sin \theta = \frac { 3 } { 5 }

A) 54\frac { 5 } { 4 }
B) 45\frac { 4 } { 5 }
C) 34\frac { 3 } { 4 }
D) 43\frac { 4 } { 3 }
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13
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(4sin⁡3t+3cos⁡2t) for 0≤t≤πx ( t ) = e ^ { - t } ( 4 \sin 3 t + 3 \cos 2 t ) \text { for } 0 \leq t \leq \pi

A) t≈0.9605t \approx 0.9605
B) t=0
C) t≈0.2632t \approx 0.2632
D)None of the above
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14
Specify the number of degrees in the indicated angle. ∞\infty

A) 150∘150 ^ { \circ }
B) 210∘210 ^ { \circ }
C) 240∘240 ^ { \circ }
D) −150∘- 150 ^ { \circ }
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Unlock for access to all 19 flashcards in this deck.
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15
Convert the indicated angle from radians to degrees. 23π12\frac { 23 \pi } { 12 }

A) 172.5∘172.5 ^ { \circ }
B) 690∘690 ^ { \circ }
C) 345∘345 ^ { \circ }
D)None of the above
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Unlock for access to all 19 flashcards in this deck.
Unlock Deck
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16
Suppose a company determines that the profit P (in hundreds of dollars)obtained from sales during week t (for 0≤t≤520 \leq t \leq 52 )of a particular year may be modeled by the trigonometric function P(t)=115−40cos⁡[π(t−17)26]P ( t ) = 115 - 40 \cos \left[ \frac { \pi ( t - 17 ) } { 26 } \right] What is the largest weekly profit?

A)$15,500
B)$23,000
C)$11,500
D)$7,500
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17
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]

A) p=3,b=−5,d=1,a=2p = 3 , b = - 5 , d = 1 , a = 2
B) p=6,b=5,d=−1,a=2p = 6 , b = 5 , d = - 1 , a = 2
C) p=3,b=5,d=1,a=2p = 3 , b = 5 , d = 1 , a = 2
D) p=6,b=−5,d=1,a=2p = 6 , b = - 5 , d = 1 , a = 2
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18
Evaluate the given expression. cos π2\frac { \pi } { 2 }

A)Undefined
B)-1
C)0
D)1
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19
Evaluate the given expression. tan 9π4\frac { 9 \pi } { 4 }

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