Question 1

Solve the problem.
-A force of 627 lb is required to pull a boat up a ramp inclined at 23° with the horizontal. How much does the boat weigh?

Accepted Answer

A) 604 lb 
B) 577 lb 
C) 2182 lb 
D) 1605 lb 
A) 604 lb 
B) 577 lb 
C) 2182 lb 
D) 1605 lb

Question 2

Find the indicated vector.
-Let $\mathbf { u } = \langle 1 , - 6 \rangle$. Find $- 9 \mathbf { u }$.

Accepted Answer

A)  $\langle - 9,54 \rangle$ 
B)  $\langle - 9 , - 54 \rangle$ 
C)  $\langle 9 , - 54 \rangle$ 
D)  $\langle 9,54 \rangle$ 
A)  $\langle - 9,54 \rangle$ 
B)  $\langle - 9 , - 54 \rangle$ 
C)  $\langle 9 , - 54 \rangle$ 
D)  $\langle 9,54 \rangle$

Question 3

Draw a sketch to represent the vector. Refer to the vectors pictured here.  
-a + d

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 4

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
-b, C, and B

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 5

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth.
-

Accepted Answer

A)  $\langle 4.7,1.82 \rangle$ 
B)  $\langle 0.94,0.34 \rangle$ 
C)  $\langle 1.71,4.7 \rangle$ 
D)  $\langle 4.7,1.71 \rangle$ 
A)  $\langle 4.7,1.82 \rangle$ 
B)  $\langle 0.94,0.34 \rangle$ 
C)  $\langle 1.71,4.7 \rangle$ 
D)  $\langle 4.7,1.71 \rangle$

Question 6

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-C = 113.6° a = 7.5 m
B = 9.6 m

Accepted Answer

A) c = 14.4 m, A = 28.4°, B = 38° 
B) c = 17.3 m, A = 30.4°, B = 36° 
C) No triangle satisfies the given conditions. 
D) c = 20.2 m, A = 26.4°, B = 40° 
A) c = 14.4 m, A = 28.4°, B = 38° 
B) c = 17.3 m, A = 30.4°, B = 36° 
C) No triangle satisfies the given conditions. 
D) c = 20.2 m, A = 26.4°, B = 40°

Question 7

Find the missing parts of the triangle.
-B = 29.5° b = 19.45
A = 19.75
If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

Accepted Answer

A) no such triangle 
B) A = 30°, C = 120.5°, c = 34.03 
C) A1 = 30°, C1 = 120.5°, c1 = 34.03; 
D) A = 150°, C = 0.5°, c = 0.34 A2 = 150°, C2 = 0.5°, c2 = 0.34 
A) no such triangle 
B) A = 30°, C = 120.5°, c = 34.03 
C) A1 = 30°, C1 = 120.5°, c1 = 34.03; 
D) A = 150°, C = 0.5°, c = 0.34 A2 = 150°, C2 = 0.5°, c2 = 0.34

Question 8

Solve the problem.
-If u = -5, 3 , v = 6, -6 , and w = -3, 12 , evaluate u ·w + v ·w.

Accepted Answer

A) -39 
B) -43 
C) -34 
D) -32 
A) -39 
B) -43 
C) -34 
D) -32

Question 9

Solve the problem.
-One rope pulls a barge directly east with a force of 42 newtons, and another rope pulls the barge directly north with a force of 68 newtons. Find the magnitude of the resultant force acting on the
Barge.

Accepted Answer

A) 110 newtons 
B) 80 newtons 
C) 2900 newtons 
D) 26 newtons 
A) 110 newtons 
B) 80 newtons 
C) 2900 newtons 
D) 26 newtons

Question 10

Find the dot product for the pair of vectors.
-$- 7 \mathbf { j } , 2 \mathbf { i }$

Accepted Answer

A)  $- 9$ 
B)  9 
C)  $- 5$ 
D)  0 
A)  $- 9$ 
B)  9 
C)  $- 5$ 
D)  0

Question 11

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-$\langle 8 \sqrt { 3 } , 8 \rangle$

Accepted Answer

A)  $16 \sqrt { 2 } ; 60 ^ { \circ }$ 
B)  $32 ; 30 ^ { \circ }$ 
C)  $16 ; 30 ^ { \circ }$ 
D)  $16 ; 150 ^ { \circ }$ 
A)  $16 \sqrt { 2 } ; 60 ^ { \circ }$ 
B)  $32 ; 30 ^ { \circ }$ 
C)  $16 ; 30 ^ { \circ }$ 
D)  $16 ; 150 ^ { \circ }$

Question 12

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth.
-

Accepted Answer

A)  $\langle-8.46,3.08\rangle$ 
B)  $\langle-0.98,0.17\rangle$ 
C)  $\langle-9,1.58)$ 
D)  $\langle-8.86,1.56\rangle$ 
A)  $\langle-8.46,3.08\rangle$ 
B)  $\langle-0.98,0.17\rangle$ 
C)  $\langle-9,1.58)$ 
D)  $\langle-8.86,1.56\rangle$

Question 13

Find the dot product for the pair of vectors.
-$\langle 5 , - 13 \rangle , \langle 15,15 \rangle$

Accepted Answer

A)  $- 195$ 
B)  270 
C)  $- 120$ 
D)  75 
A)  $- 195$ 
B)  270 
C)  $- 120$ 
D)  75

Question 14

Graph the polar equation for in [0°, 360°).
-A trigonometry student makes the statement, "If we know any two sides and one angle of a
triangle, then the triangle is uniquely determined." Is this a valid statement? Explain,
referring to the congruence axioms.

Accepted Answer

No. Explan

Question 15

Graph the polar equation for in [0°, 360°).
-State the formulas for the area of a triangle ABC that were derived using the law of sines.

Accepted Answer

The answer of Graph the polar equation for in [0°,...

Question 16

Draw a sketch to represent the vector. Refer to the vectors pictured here.  
-3d

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 17

Solve the problem.
-Points A and B are on opposite sides of a lake. Point C is 80.7 meters from A. The measure of angle BAC is 72°20', and the measure of angle ACB is determined to be 35°50'. Find the distance between
Points A and B (to the nearest meter).

Accepted Answer

A) 23 m 
B) 25 m 
C) 48 m 
D) 50 m 
A) 23 m 
B) 25 m 
C) 48 m 
D) 50 m

Question 18

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth.
-

Accepted Answer

A)  $\langle - 7.78,7.78 \rangle$ 
B)  $\langle - 8.43,7.0 \rangle \rangle$ 
C)  $\langle - 0.77,0.64 \rangle$ 
D)  $\langle - 7.07,8.43 \rangle$ 
A)  $\langle - 7.78,7.78 \rangle$ 
B)  $\langle - 8.43,7.0 \rangle \rangle$ 
C)  $\langle - 0.77,0.64 \rangle$ 
D)  $\langle - 7.07,8.43 \rangle$

Question 19

Solve the problem.
-A box weighing 64 lb is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of 27 lb. What angle, to the nearest degree, does the first rope make with the
Vertical?

Accepted Answer

A) 46° 
B) 23° 
C) 12° 
D) 35° 
A) 46° 
B) 23° 
C) 12° 
D) 35°

Question 20

Sketch the vectors u and w with angle between them and sketch the resultant.
-$$| \mathbf { u } | = 10 , | \mathbf { w } | = 4 , \theta = 40 ^ { \circ }$$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Solve the problem. -A force of 627 lb is required to pull a boat up a ramp inclined at 23° with the horizontal. How much does the boat weigh?

Find the indicated vector. -Let $\mathbf { u } = \langle 1 , - 6 \rangle$ . Find $- 9 \mathbf { u }$ .

Draw a sketch to represent the vector. Refer to the vectors pictured here. -a + d

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -b, C, and B

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -C = 113.6° a = 7.5 m B = 9.6 m

Find the missing parts of the triangle. -B = 29.5° b = 19.45 A = 19.75 If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

Solve the problem. -If u = -5, 3 , v = 6, -6 , and w = -3, 12 , evaluate u ·w + v ·w.

Solve the problem. -One rope pulls a barge directly east with a force of 42 newtons, and another rope pulls the barge directly north with a force of 68 newtons. Find the magnitude of the resultant force acting on the Barge.

Find the dot product for the pair of vectors. - $- 7 \mathbf { j } , 2 \mathbf { i }$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - $\langle 8 \sqrt { 3 } , 8 \rangle$

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Find the dot product for the pair of vectors. - $\langle 5 , - 13 \rangle , \langle 15,15 \rangle$

Graph the polar equation for in [0°, 360°). -A trigonometry student makes the statement, "If we know any two sides and one angle of a triangle, then the triangle is uniquely determined." Is this a valid statement? Explain, referring to the congruence axioms.

Graph the polar equation for in [0°, 360°). -State the formulas for the area of a triangle ABC that were derived using the law of sines.

Draw a sketch to represent the vector. Refer to the vectors pictured here. -3d

Solve the problem. -Points A and B are on opposite sides of a lake. Point C is 80.7 meters from A. The measure of angle BAC is 72°20', and the measure of angle ACB is determined to be 35°50'. Find the distance between Points A and B (to the nearest meter).

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Solve the problem. -A box weighing 64 lb is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of 27 lb. What angle, to the nearest degree, does the first rope make with the Vertical?

Sketch the vectors u and w with angle between them and sketch the resultant. - $| \mathbf { u } | = 10 , | \mathbf { w } | = 4 , \theta = 40 ^ { \circ }$

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 7: Applications of Trigonometry and Vectors

Solve the problem. -A force of 627 lb is required to pull a boat up a ramp inclined at 23° with the horizontal. How much does the boat weigh?

Find the indicated vector. -Let u=⟨1,−6⟩\mathbf { u } = \langle 1 , - 6 \rangleu=⟨1,−6⟩ . Find −9u- 9 \mathbf { u }−9u .

Draw a sketch to represent the vector. Refer to the vectors pictured here. -a + d

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -b, C, and B

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -C = 113.6° a = 7.5 m B = 9.6 m

Find the missing parts of the triangle. -B = 29.5° b = 19.45 A = 19.75 If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

Solve the problem. -If u = -5, 3 , v = 6, -6 , and w = -3, 12 , evaluate u ·w + v ·w.

Solve the problem. -One rope pulls a barge directly east with a force of 42 newtons, and another rope pulls the barge directly north with a force of 68 newtons. Find the magnitude of the resultant force acting on the Barge.

Find the dot product for the pair of vectors. - −7j,2i- 7 \mathbf { j } , 2 \mathbf { i }−7j,2i

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - ⟨83,8⟩\langle 8 \sqrt { 3 } , 8 \rangle⟨83​,8⟩

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Find the dot product for the pair of vectors. - ⟨5,−13⟩,⟨15,15⟩\langle 5 , - 13 \rangle , \langle 15,15 \rangle⟨5,−13⟩,⟨15,15⟩

Graph the polar equation for in [0°, 360°). -A trigonometry student makes the statement, "If we know any two sides and one angle of a triangle, then the triangle is uniquely determined." Is this a valid statement? Explain, referring to the congruence axioms.

Graph the polar equation for in [0°, 360°). -State the formulas for the area of a triangle ABC that were derived using the law of sines.

Draw a sketch to represent the vector. Refer to the vectors pictured here. -3d

Solve the problem. -Points A and B are on opposite sides of a lake. Point C is 80.7 meters from A. The measure of angle BAC is 72°20', and the measure of angle ACB is determined to be 35°50'. Find the distance between Points A and B (to the nearest meter).

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Solve the problem. -A box weighing 64 lb is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of 27 lb. What angle, to the nearest degree, does the first rope make with the Vertical?

Sketch the vectors u and w with angle between them and sketch the resultant. - ∣u∣=10,∣w∣=4,θ=40∘| \mathbf { u } | = 10 , | \mathbf { w } | = 4 , \theta = 40 ^ { \circ }∣u∣=10,∣w∣=4,θ=40∘

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Graphs of the Circular Functions

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Find the indicated vector. -Let $\mathbf { u } = \langle 1 , - 6 \rangle$ . Find $- 9 \mathbf { u }$ .

Find the dot product for the pair of vectors. - $- 7 \mathbf { j } , 2 \mathbf { i }$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. - $\langle 8 \sqrt { 3 } , 8 \rangle$

Find the dot product for the pair of vectors. - $\langle 5 , - 13 \rangle , \langle 15,15 \rangle$

Sketch the vectors u and w with angle between them and sketch the resultant. - $| \mathbf { u } | = 10 , | \mathbf { w } | = 4 , \theta = 40 ^ { \circ }$