AnswersAlgebra 2 MP 234 CHSEvaluating the Six Trigonometric Functions

Evaluating the Six Trigonometric Functions — Unit test Answers

15 verified answers
1
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Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.Trigonometric area formula: Area =

Question illustration
A
17 feet
B
33 feet
C
40 feet
D
50 feet
2
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Trigonometric area formula: Area =

Question illustration
A
70.5 square units
B
111.3 square units
C
185.4 square units
D
222.5 square units
3

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

Question illustration
A
(–5, 12)
B
(5, –12)
C
(–12, 5)
D
(12, –5)
4

Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

Question illustration
A
The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option A
B
The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
Option B
C
The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.
Option C
D
The values of sin and cos represent the legs of a right triangle with a hypotenuse of –1, since is in Quadrant II; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option D
5

If , which of the following represents approximate values of and , for ?

Question illustration
A
sine theta almost-equals 0.9511; tangent theta almost equals 0.3249
Option A
B
sine theta almost-equals 0.9511; tangent theta almost equals 3.0780
Option B
C
sine theta almost-equals 3.2362; tangent theta almost-equals 0.0955
Option C
D
sine theta almost-equals 3.2362; tangent theta almost-equals 10.4731
Option D
6

The point P(x, y) is on the terminal ray of angle . If is between radians and radians and csc = , what are the coordinates of P(x, y)?

Question illustration
A
P(, –2)
Option A
B
P (, –2)
Option B
C
P(–2, )
Option C
D
P(–2, )
Option D
7

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.Heron’s formula: Area =

Question illustration
A
31 square inches
B
34 square inches
C
48 square inches
D
62 square inches
8

Heron’s formula: Area =

Question illustration
A
27 square units
B
38 square units
C
364 square units
D
728 square units
9

Law of sines:

Question illustration
A
2.9 units
B
3.8 units
C
5.1 units
D
6.2 units
10

The law of cosines is used to find the measure of .

Question illustration
A
44º
B
49º
C
54º
D
59º
11

A spinner for a board game consists of a cardboard circle with two plastic arrows anchored to its center. The arrows are congruent isosceles triangles connected at their bases, as shown.Heron’s formula: Area =

Question illustration
A
3.9 square centimeters
B
6.7 square centimeters
C
7.7 square centimeters
D
13.4 square centimeters
12

The point is the point at which the terminal ray of angle intersects the unit circle. What are the values for the cosine and cotangent functions for angle ?

Question illustration
A
cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative 1
Option A
B
cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = 1
Option B
C
cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative one-half
Option C
D
cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = one-half
Option D
13

What is the length of line segment RS? Use the law of sines to find the answer. Round to the nearest tenth.

Question illustration
A
2.2 units
B
2.4 units
C
3.0 units
D
3.3 units
14

Heron’s formula: Area =

Question illustration
A
17.75 square units
B
81.33 square units
C
372.71 square units
D
957.74 square units
15

On which triangle can the law of cosines be used to find the length of an unknown side?Law of cosines: a2 = b2 + c2 – 2bccos(A)

A
Triangle Q R S is shown. The length of Q R is s, the length of R S is q, and the length of Q S is 12. Angle R Q S is 36 degrees, angle Q S R is 57 degrees, and angle S R Q is 87 degrees.
Option A
B
Triangle Q R S is shown. The length of Q R is s, the length of R S is 7, and the length of Q S is 12. Angle R S Q is 57 degrees.
Option B
C
Triangle Q R S is shown. The length of Q R is s, the length of R S is 7, and the length of Q S is b. Angle R S Q is 57 degrees and angle S Q R is 36 degrees.
Option C
D
Triangle Q R S is shown. The length of Q R is s, the length of R S is q, and the length of Q S is 12. Angle R Q S is 36 degrees and angle Q S R is 57 degrees.
Option D

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