Answers PrecalculusEquations of Ellipses

Equations of Ellipses — Unit test Answers

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What is the equation of the graph below?

y = sec(x) + 2

y = csc(x) + 2

y = csc(x + 2)

y = sec(x + 2)

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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?

(–5, 12)

(5, –12)

(–12, 5)

(12, –5)

Which transformation should be applied to the graph of the function to obtain the graph of the function ?

a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up

a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30

Which of the following best explains the value of on the unit circle below?

The length opposite the angle is the vertical distance from the x-axis on the graph.

The length adjacent to the angle is the vertical distance from the x-axis on the graph.

The length opposite the angle is the horizontal distance from the y-axis on the graph.

The length adjacent to the angle is the horizontal distance from the y-axis on the graph.

What is the radius of a circle whose equation is (x + 5)2 + (y – 3)2 = 42?

2 units

4 units

8 units

16 units

Which equation represents a hyperbola with a center at (0, 0), a vertex at (−48, 0), and a focus at (50, 0)?

= 1

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

sine theta almost-equals 0.9511; tangent theta almost equals 0.3249

sine theta almost-equals 0.9511; tangent theta almost equals 3.0780

sine theta almost-equals 3.2362; tangent theta almost-equals 0.0955

sine theta almost-equals 3.2362; tangent theta almost-equals 10.4731

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.

Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.

Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.

Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.

Which of the following could be the equation of the function below?

y = negative 3 sine (2 (x + pi)) + 2

y = negative 3 sine (x + pi) + 2

y = 3 sine (4 (x minus pi)) + 4

y = 3 sine (2 (x + pi)) + 2

A point is on a circle if the distance from the center of the circle to the point is equal to the

area.

circumference.

radius.

diameter.

Question text not available

x = −4.25 and x = 8.25

x = −3.25 and x = 9.25

y = −4.25 and y = 8.25

y = −3.25 and y = 9.25

Which function describes the graph below?

f (x) = 6 cosine (x)

f (x) = 3 cosine (x) + 3

f (x) = 6 sine (x)

f (x) = 3 sine (x) + 3

The center of a hyperbola is located at the origin. One focus is located at (0, 20), and its associated directrix is represented by the line y = . What is the equation of the hyperbola?