AnswersGA-Advanced Algebra Concepts and Connections CREvaluating the Six Trigonometric Functions

Lesson 6: Evaluating the Six Trigonometric Functions Answers

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1
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Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

Answers:
sin(θ) =:-15/17
cos(θ) =:8/17
tan(θ) =:-15/8
csc(θ) =:-17/15
sec(θ) =:17/8
cot(θ) =:-8/15
2
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-15/8-15/17✔ 8/178

A
-15/8
B
-15/17
C
✔ 8/17
D
8
3

✔ -15/8-15/178/17-8/15

A
✔ -15/8
B
-15/17
C
8/17
D
-8/15
4

-15/17✔ -17/1517/15-17/8

A
-15/17
B
✔ -17/15
C
17/15
D
-17/8
5

-8/17-15/178/17✔ 17/8

A
-8/17
B
-15/17
C
8/17
D
✔ 17/8
6

-15/8-15/17✔ -8/158/17

A
-15/8
B
-15/17
C
✔ -8/15
D
8/17
7

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

Answers:
sin(θ) =:-15/17
cos(θ) =:8/17
tan(θ) =:-15/8
csc(θ) =:-17/15
sec(θ) =:17/8
cot(θ) =:-8/15
8

Which value(s) are incorrect?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
E
Option
Option E
F
Option
Option F
9

Question text not available

Question illustration
A
Option
Option A
B
Option
Option B
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Option
Option C
D
Option
Option D
10

Use the identity sin²(A) + cos²(A) = 1✔ tan²(A) + 1 = sec²(A)1 + cot²(A) = csc²(A)

A
sin²(A) + cos²(A) = 1
B
✔ tan²(A) + 1 = sec²(A)
C
1 + cot²(A) = csc²(A)
11

Solving the identity, tan(A) = _____.

A
Option
Option A
B
Option
Option B
C
Option
Option C
12

Question text not available

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

Question text not available

Answer:

To find the values of the six trigonometric functions for the angle θ with the terminal side passing through (5, –2), first identify the coordinates x = 5 and y = –2. Since the x-coordinate is positive and the y-coordinate is negative, the point is in Quadrant IV. Next, calculate the radius (r) using the Pythagorean theorem: r = √(5² + (–2)²) = √(25 + 4) = √29. Then apply the trigonometric definitions: sin(θ) = y/r = –2/√29 = –2√29/29 cos(θ) = x/r = 5/√29 = 5√29/29 tan(θ) = y/x = –2/5 csc(θ) = r/y = –√29/2 sec(θ) = r/x = √29/5 cot(θ) = x/y = –5/2

14

Question text not available

Question illustration
Answer:

-1

15

to find the value of (A).

Answer:

tan

16

What is cot(A)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
17

Which did you include in your response?

A
Plot the point (5, –2) and draw a line from the point to the x-axis to make a right triangle.
B
Use the Pythagorean theorem to find the length of the hypotenuse.
C
Use the definition of each trigonometric function to find the values.
D
Determine the appropriate sign for each function, using the fact that the terminal side is in Quadrant IV.

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