Question 1

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant.
-$$| \mathbf { u } | = 2.85 , | \mathbf { w } | = 2.85 , \theta = 90 ^ { \circ }$$

Accepted Answer

A) 
  
B)

Question 2

Solve the problem.
-If u =-3, 5 and v =4, -2 , evaluate u · (5v).

Accepted Answer

A)  -115 
B)  -110 
C)  -107 
D)  -38 
A)  -115 
B)  -110 
C)  -107 
D)  -38

Question 3

Write the complex number in trigonometric form r(c $$r ( \cos \theta + i \sin \theta )$$ ), with $$\theta$$ in the interval [0 $$\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$$
-$- 4 - 4 i \sqrt { 3 }$

Accepted Answer

A)  $8 \left( \cos 290 ^ { \circ } + i \sin 290 ^ { \circ } \right)$ 
B)  $4 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$ 
C)  $8 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$ 
D)  $8 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$ 
A)  $8 \left( \cos 290 ^ { \circ } + i \sin 290 ^ { \circ } \right)$ 
B)  $4 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$ 
C)  $8 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$ 
D)  $8 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$

Question 4

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-A force of $639 \mathrm { lb }$ is required to pull a boat up a ramp inclined at $27 ^ { \circ }$ with the horizontal. How much does the boat weigh?

Accepted Answer

A)  $569 \mathrm { lb }$ 
B)  $1977 \mathrm { lb }$ 
C)  $1408 \mathrm { lb }$ 
D)  $612 \mathrm { lb }$ 
A)  $569 \mathrm { lb }$ 
B)  $1977 \mathrm { lb }$ 
C)  $1408 \mathrm { lb }$ 
D)  $612 \mathrm { lb }$

Question 5

Graph the polar equation for $$\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$$
-$$r = 7 \cos 5 \theta$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 3 } - 8 = 0$$

Accepted Answer

A)  $\left\{ 2,2 \operatorname { cis } 120 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } \right\}$ 
B)  $\left\{ 2,2 \operatorname { cis } 60 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$ 
C)  $\left\{ 2,2 \operatorname { cis } 300 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$ 
D)  $\left\{ 2,2 \right.$ cis $60 ^ { \circ } , 2$ cis $\left. 240 ^ { \circ } \right\}$ 
A)  $\left\{ 2,2 \operatorname { cis } 120 ^ { \circ } , 2 \operatorname { cis } 240 ^ { \circ } \right\}$ 
B)  $\left\{ 2,2 \operatorname { cis } 60 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$ 
C)  $\left\{ 2,2 \operatorname { cis } 300 ^ { \circ } , 2 \operatorname { cis } 300 ^ { \circ } \right\}$ 
D)  $\left\{ 2,2 \right.$ cis $60 ^ { \circ } , 2$ cis $\left. 240 ^ { \circ } \right\}$

Question 7

Provide an appropriate response.
-Why can't the Pythagorean theorem be used to solve an oblique triangle?

Accepted Answer

The Pythagorean theo

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 2.85 , | \mathbf { w } | = 2.85 , \theta = 90 ^ { \circ }$

Solve the problem. -If u =-3, 5 and v =4, -2 , evaluate u · (5v).

Write the complex number in trigonometric form r(c $r ( \cos \theta + i \sin \theta )$ ), with $\theta$ in the interval [0 $\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $- 4 - 4 i \sqrt { 3 }$

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place. -A force of $639 \mathrm { lb }$ is required to pull a boat up a ramp inclined at $27 ^ { \circ }$ with the horizontal. How much does the boat weigh?

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 7 \cos 5 \theta$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 7 \cos 5 \theta$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 3 } - 8 = 0$

Provide an appropriate response. -Why can't the Pythagorean theorem be used to solve an oblique triangle?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 9: Applications of Trigonometry

Sketch the vectors u and w with angle θ\thetaθ between them and sketch the resultant. - ∣u∣=2.85,∣w∣=2.85,θ=90∘| \mathbf { u } | = 2.85 , | \mathbf { w } | = 2.85 , \theta = 90 ^ { \circ }∣u∣=2.85,∣w∣=2.85,θ=90∘