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

Evaluating the Six Trigonometric Functions Answers

28 verified answers4 views
1
Free Preview

Which of the following describe the sine function? Check all that apply.

A
Its range is all real numbers.
B
Its period is .
Option B
C
Its maximum is –1.
D
Its domain is all real numbers.
E
Its maximum is 1.
2
Free Preview

An x-intercept is for .

Question illustration
A
the sine function
B
the cosine function
C
both the sine and cosine function
3

The minimum value is –1 for .

Question illustration
A
the sine function
B
the cosine function
C
both the sine and cosine function
4

An x-intercept is for .

Question illustration
A
the sine function
B
the cosine function
C
both the sine and cosine function
5

Based on these results, changing the sign of a the maximum and minimum values of the graph of y = asin(x).

A
has no effect on
B
increases
C
decreases
6

The domain is all real numbers for .

A
the sine function
B
the cosine function
C
both the sine and cosine function
7

Complete the following statements for the cosine function shown in the graph.The minimum value is .

A
–1
B
–0.75
C
–0.5
D
–0.25
8

The amplitude is .

A
0.25
B
0.5
C
0.75
D
1
9

The graph shows the function .

Question illustration
A
y = sin(x) + 6
B
y = cos(x) – 6
C
y = sin(x) – 6
D
y = cos(x) + 6
10

Identify the transformations needed to graph the cosine function y = –0.5cos(x) – 3 from the parent cosine function. Check all that apply.

A
vertical compression by a factor of 0.5
B
reflection across the y-axis
C
vertical translation 3 units down
D
vertical stretch by a factor of 0.5
E
reflection across the x-axis
F
vertical translation 3 units up
G
vertical translation 0.5 units down
11

Complete the following statements for the cosine function shown in the graph.The minimum value is .

A
–1
B
–0.75
C
–0.5
D
–0.25
12

An equation for this function is .

A
y = 0.75cos(x)
B
y = –0.75cos(x)
C
y = cos(0.75x)
D
y = cos(–0.75x)
13

Use the graph to identify the amplitude for each function shown.The amplitude of the function shown in orange is .

A
–6
B
–4
C
–3
D
3
E
4
F
6
14

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 xcoordinate is positive and the ycoordinate 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

15

The graph shows the function .

Question illustration
A
y = sin(x) + 6
B
y = cos(x) – 6
C
y = sin(x) – 6
D
y = cos(x) + 6
16

Identify the transformations needed to graph the cosine function y = –0.5cos(x) – 3 from the parent cosine function. Check all that apply.

A
vertical compression by a factor of 0.5
B
reflection across the y-axis
C
vertical translation 3 units down
D
vertical stretch by a factor of 0.5
E
reflection across the x-axis
F
vertical translation 3 units up
G
vertical translation 0.5 units down
17

The maximum value is .

A
0.25
B
0.5
C
0.75
D
1
18

The function rule y = cos(x) + 2 describes graph shown here.

Question illustration
A
a
B
b
C
c
D
d
19

The function rule y = –0.5cos(x) – 3 describes graph shown.

Question illustration
A
a
B
b
C
c
D
d
20

The maximum value is .

A
0.25
B
0.5
C
0.75
D
1

Did you find these answers helpful?

More from this Course

Instruction
35 verified answers

Instruction

Instruction
29 verified answers

Instruction

Instruction
28 verified answers

Graphing Sine and Cosine