Question 1

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for
the graph.
- 
$[ - 5,5 ]$ by $[ - 5,5 ]$

Accepted Answer

A)  $r = 2 + 2 \cos \theta$ 
B)  $r = 2 + 3 \cos \theta$ 
C)  $r = 3 + 2 \cos \theta$ 
D)  $r = 4 + \cos \theta$ 
A)  $r = 2 + 2 \cos \theta$ 
B)  $r = 2 + 3 \cos \theta$ 
C)  $r = 3 + 2 \cos \theta$ 
D)  $r = 4 + \cos \theta$

Question 2

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°.
-$( 3 , - 3 )$

Accepted Answer

A)  $\left( 3 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 225 ^ { \circ } \right)$ 
B)  $\left( 3 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
C)  $\left( 3 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 3 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
A)  $\left( 3 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 225 ^ { \circ } \right)$ 
B)  $\left( 3 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
C)  $\left( 3 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 3 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 45 ^ { \circ } \right)$

Question 3

Find an equivalent equation in polar coordinates.
-$$x ^ { 2 } + y ^ { 2 } - 4 x = 0$$

Accepted Answer

A)  $r \sin ^ { 2 } \theta = 4 \cos \theta$ 
B)  $r \cos ^ { 2 } \theta = 4 \sin \theta$ 
C)  $r = 4 \cos \theta$ 
D)  $r = 4 \sin \theta$ 
A)  $r \sin ^ { 2 } \theta = 4 \cos \theta$ 
B)  $r \cos ^ { 2 } \theta = 4 \sin \theta$ 
C)  $r = 4 \cos \theta$ 
D)  $r = 4 \sin \theta$

Question 4

Solve the problem.
-Find the work done by a force $F$ of 40 pounds acting in the direction $\langle 3,5 \rangle$ in moving an object 7 feet from $( 0,0 )$ to a point in the first quadrant along the line $y = x$.

Accepted Answer

A)  $\approx 144.06$ foot-pounds 
B)  $\approx 271.64$ foot-pounds 
C)  $\approx 1583.92$ foot-pounds 
D)  $\approx 384.16$ foot-pounds 
A)  $\approx 144.06$ foot-pounds 
B)  $\approx 271.64$ foot-pounds 
C)  $\approx 1583.92$ foot-pounds 
D)  $\approx 384.16$ foot-pounds

Question 5

Write the complex number in the form a + bi.
-$4 \left( \cos - 135 ^ { \circ } + i \sin - 135 ^ { \circ } \right)$

Accepted Answer

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

Question 6

Use the given graph to find the values of t that produce the graph in the given quadrant.
-$x=4-|t|, y=t-3,-6 \leq t \leq 6$

Quadrant IV

Accepted Answer

A)  $- 6 \leq t \leq - 4$ 
B)  $- 4 \leq t \leq 3$ 
C)  $4 \leq t \leq 6$ 
D)  $3 \leq t \leq 4$ 
A)  $- 6 \leq t \leq - 4$ 
B)  $- 4 \leq t \leq 3$ 
C)  $4 \leq t \leq 6$ 
D)  $3 \leq t \leq 4$

Question 7

Find the component form and magnitude of the indicated vector.
-Given that $P = ( 5,1 )$ and $Q = ( 4,6 )$, find the component form and magnitude of the vector $\overrightarrow { Q P }$.

Accepted Answer

A)  $\langle 1 , - 5 \rangle , 26$ 
B)  $( 1 , - 5 \rangle , \sqrt { 26 }$ 
C)  $\langle - 1,5 \rangle , 26$ 
D)  $\langle - 1,5 \rangle , \sqrt { 26 }$ 
A)  $\langle 1 , - 5 \rangle , 26$ 
B)  $( 1 , - 5 \rangle , \sqrt { 26 }$ 
C)  $\langle - 1,5 \rangle , 26$ 
D)  $\langle - 1,5 \rangle , \sqrt { 26 }$

Question 8

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.
-Let $\mathbf { u } = \langle 5,3 \rangle$. Find the unit vector in the direction of $\mathbf { u }$, and write your answer in component form.

Accepted Answer

A)  $\langle 1,1 \rangle$ 
B)  $\left\langle \frac { 5 } { 8 } , \frac { 3 } { 8 } \right\rangle$ 
C)  $\left( \frac { 5 } { 34 } , \frac { 3 } { 34 } \right)$ 
D)  $\left. \mid \frac { 5 } { \sqrt { 34 } } , \frac { 3 } { \sqrt { 34 } } \right)$ 
A)  $\langle 1,1 \rangle$ 
B)  $\left\langle \frac { 5 } { 8 } , \frac { 3 } { 8 } \right\rangle$ 
C)  $\left( \frac { 5 } { 34 } , \frac { 3 } { 34 } \right)$ 
D)  $\left. \mid \frac { 5 } { \sqrt { 34 } } , \frac { 3 } { \sqrt { 34 } } \right)$

Question 9

Express the complex number in polar form.
-

Accepted Answer

A)  $7 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ 
B)  $7 \left( \sin 60 ^ { \circ } + i \cos 60 ^ { \circ } \right)$ 
C)  $7 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ 
D)  $7 \left( \cos 60 ^ { \circ } + \sin 60 ^ { \circ } \right)$ 
A)  $7 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ 
B)  $7 \left( \sin 60 ^ { \circ } + i \cos 60 ^ { \circ } \right)$ 
C)  $7 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ 
D)  $7 \left( \cos 60 ^ { \circ } + \sin 60 ^ { \circ } \right)$

Question 10

Find an equivalent equation in rectangular coordinates.
-$r = 2 ( \sin \theta - \cos \theta )$

Accepted Answer

A)  $2 x ^ { 2 } + 2 y ^ { 2 } = y - x$ 
B)  $x ^ { 2 } + y ^ { 2 } = 2 y - 2 x$ 
C)  $x ^ { 2 } + y ^ { 2 } = 2 x - 2 y$ 
D)  $2 x ^ { 2 } + 2 y ^ { 2 } = x - y$ 
A)  $2 x ^ { 2 } + 2 y ^ { 2 } = y - x$ 
B)  $x ^ { 2 } + y ^ { 2 } = 2 y - 2 x$ 
C)  $x ^ { 2 } + y ^ { 2 } = 2 x - 2 y$ 
D)  $2 x ^ { 2 } + 2 y ^ { 2 } = x - y$

Question 11

Express the complex number in polar form.
-$3 - 3 i$

Accepted Answer

A)  $3 \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$ 
B)  $3 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
C)  $3 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
D)  $3 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$ 
A)  $3 \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$ 
B)  $3 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
C)  $3 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
D)  $3 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$

Question 12

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle 9,3 \rangle$. Find $9 \mathbf { u }$.

Accepted Answer

A)  $\langle - 81,2 \rangle \rangle$ 
B)  $\langle - 81 , - 27 \rangle$ 
C)  $\langle 81,27 \rangle$ 
D)  $\langle 81 , - 27 \rangle$ 
A)  $\langle - 81,2 \rangle \rangle$ 
B)  $\langle - 81 , - 27 \rangle$ 
C)  $\langle 81,27 \rangle$ 
D)  $\langle 81 , - 27 \rangle$

Question 13

Find the component form of the vector v.
-

Accepted Answer

A)  $\approx \langle - 15.84 , - 46 \rangle$ 
B)  $\approx ( - 43.49 , - 14.98 \rangle$ 
C)  $\approx \langle - 14.98 , - 43.49 \rangle$ 
D)  $\approx \langle - 0.33 , - 0.95 \rangle$ 
A)  $\approx \langle - 15.84 , - 46 \rangle$ 
B)  $\approx ( - 43.49 , - 14.98 \rangle$ 
C)  $\approx \langle - 14.98 , - 43.49 \rangle$ 
D)  $\approx \langle - 0.33 , - 0.95 \rangle$

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - $( 3 , - 3 )$

Find an equivalent equation in polar coordinates. - $x ^ { 2 } + y ^ { 2 } - 4 x = 0$

Solve the problem. -Find the work done by a force $F$ of 40 pounds acting in the direction $\langle 3,5 \rangle$ in moving an object 7 feet from $( 0,0 )$ to a point in the first quadrant along the line $y = x$ .

Write the complex number in the form a + bi. - $4 \left( \cos - 135 ^ { \circ } + i \sin - 135 ^ { \circ } \right)$

Use the given graph to find the values of t that produce the graph in the given quadrant. - $x=4-|t|, y=t-3,-6 \leq t \leq 6$ $Use the given graph to find the values of t that produce the graph in the given quadrant. - x=4-|t|, y=t-3,-6 \leq t \leq 6 Quadrant IV$ Quadrant IV

Find the component form and magnitude of the indicated vector. -Given that $P = ( 5,1 )$ and $Q = ( 4,6 )$ , find the component form and magnitude of the vector $\overrightarrow { Q P }$ .

Find the unit vector in the direction of the given vector. Write your answer in the indicated form. -Let $\mathbf { u } = \langle 5,3 \rangle$ . Find the unit vector in the direction of $\mathbf { u }$ , and write your answer in component form.

Express the complex number in polar form. -

Find an equivalent equation in rectangular coordinates. - $r = 2 ( \sin \theta - \cos \theta )$

Express the complex number in polar form. - $3 - 3 i$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 9,3 \rangle$ . Find $9 \mathbf { u }$ .

Find the component form of the vector v. -

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Exam 6: Applications of Trigonometry

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - [−5,5][ - 5,5 ][−5,5] by [−5,5][ - 5,5 ][−5,5]

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - (3,−3)( 3 , - 3 )(3,−3)

Find an equivalent equation in polar coordinates. - x2+y2−4x=0x ^ { 2 } + y ^ { 2 } - 4 x = 0x2+y2−4x=0

Solve the problem. -Find the work done by a force FFF of 40 pounds acting in the direction ⟨3,5⟩\langle 3,5 \rangle⟨3,5⟩ in moving an object 7 feet from (0,0)( 0,0 )(0,0) to a point in the first quadrant along the line y=xy = xy=x .

Write the complex number in the form a + bi. - 4(cos⁡−135∘+isin⁡−135∘)4 \left( \cos - 135 ^ { \circ } + i \sin - 135 ^ { \circ } \right)4(cos−135∘+isin−135∘)

Use the given graph to find the values of t that produce the graph in the given quadrant. - x=4−∣t∣,y=t−3,−6≤t≤6x=4-|t|, y=t-3,-6 \leq t \leq 6x=4−∣t∣,y=t−3,−6≤t≤6 Quadrant IV

Find the component form and magnitude of the indicated vector. -Given that P=(5,1)P = ( 5,1 )P=(5,1) and Q=(4,6)Q = ( 4,6 )Q=(4,6) , find the component form and magnitude of the vector QP→\overrightarrow { Q P }QP​ .

Find the unit vector in the direction of the given vector. Write your answer in the indicated form. -Let u=⟨5,3⟩\mathbf { u } = \langle 5,3 \rangleu=⟨5,3⟩ . Find the unit vector in the direction of u\mathbf { u }u , and write your answer in component form.