AnswersPrecalculusGeneral Form of Sine and Cosine

General Form of Sine and Cosine — Quiz Answers

10 verified answers2 views
1
Free Preview

Review the given functions. j times x is equal to 51 cosine open paren x plus pi over 2 close paren plus 24 k times x is equal to 51 cosine open paren x minus 3 pi over 4 close paren plus 24 What is the transformation of function j times x to function k times x ?

A
a shift left pi over 4 units
B
a shift left 5 pi over 4 units
C
a shift right 5 pi over 4 units
D
a shift right pi over 4 units
2
Free Preview

Suppose the function f of t is equal to 95 cosine open paren pi over 10 t close paren plus 120 models the height of a seat on a Ferris wheel after t minutes. Based on this information, what is the diameter of the Ferris wheel?

A
215 ft
B
95 ft
C
120 ft
D
190 ft
3

Consider the graphs of f of x is equal to 5 sine open paren 2 x minus pi over 3 close paren minus 9 and g of x is equal to 5 sine open paren 2 x minus pi over 8 close paren minus 9 Which feature of the graph of g of x is different from the graph of f of x ?

A
the period
B
the amplitude
C
the phase shift
D
the vertical shift
4

The water depth in a harbor rises and falls over time. The function f of t is equal to 4 point 1 sine open paren pi over 6 t minus pi over 3 close paren plus 19 point 7 models the water depth, in feet, after t hours. During the first 24 hours, at what times does the water depth reach a maximum?

A
at 11 and 23 hours
B
at 5 , 11 , 17 , and 23 hours
C
at 2 , 8 , 14 , and 20 hours
D
at 5 and 17 hours
5

An object travels back and forth along a straight line. Its velocity, in centimeters per second, is given by the function v times t is equal to 13 sine open paren pi over 45 t close paren , where t is time in seconds. What is the maximum velocity of the object?

A
90 cm/s
B
26 cm/s
C
13 cm/s
D
0 cm/s
6

Consider the function h of x is equal to negative 2 cosine open paren 8 x minus pi over 4 close paren plus 5 What transformation results in j times x is equal to negative 2 cosine open paren 8 x minus pi over 4 close paren minus 5 ?

A
translating 10 units down
B
reflecting across the y -axis
C
translating 5 units down
D
reflecting across the x -axis
7

Which graph represents the function h of x is equal to 2 sine open paren x plus pi over 2 close paren minus 1 ?

A
Image with description On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, 1).
B
Image with description On a coordinate plane, a function has a maximum of 0 and minimum of negative 2. It completes one period at 2 pi. It crosses the y-axis at (0, 0).
C
Image with description On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, negative 3).
D
Image with description On a coordinate plane, a function has a maximum of 1 and minimum of negative 1. It completes one period at 2 pi. It crosses the y-axis at (0, 1).
8

Which graph represents the function g of x is equal to 7 cosine x after a shift of 5 pi over 3 units to the right?

A
Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It decreases through the y-axis at (0, 4).
B
Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, 6).
C
Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, negative 6).
D
Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It increases through the y-axis at (0, 4).
9

A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y is equal to 6 cosine open paren 2 comma 000 pi x close paren plus 11 , where x is time in minutes. How many times does the fan rotate each minute?

A
1 comma 000
B
6 comma 000
C
4 comma 000
D
2 comma 000
10

Which graph represents the function y is equal to sine of open paren 1 half x close paren after a shift of 3 units down?

A
Image with description On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at 4 pi. It crosses the y-axis at (0, negative 2).
B
Image with description On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at pi. It crosses the y-axis at (0, negative 2).
C
Image with description On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at pi. It increases through the y-axis at (0, negative 3).
D
Image with description On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at 4 pi. It increases through the y-axis at (0, negative 3).

Did you find these answers helpful?

More from this Course

Quiz
20 verified answers

Quiz

Quiz
20 verified answers

Quiz

Quiz
10 verified answers

Quiz