Math_ASS

9/28/2020 Southern New Hampshire University -

9/28/2020 Southern New Hampshire University -

Question 1: (3 points)

Find the center and the radius of the circle with the equation

x2 + 10 x + y 2 + 10 y − 94 = 0

Enter the center as an ordered pair (x, y).

The center is __________

The radius is ____________

Question 2: (5 points)

Consider the value of the trigonometric function sin ( )

It's value is

__________

Now find the exact value of that trigonometric function.

sin ( ) = __________

Show your work and explain, in your own words, how you arrived at your answers.

__________

Question 3: (3 points)

Find the reference angle, the quadrant of the terminal side, and the sine and cosine of 135°.

Enter the exact answers.

The terminal side of the angle 135° lies in quadrant __________.

Its reference angle is ____________ °.

sin (135°) = __________ cos (135°) = __________

Question 4: (3 points)

Find the reference angle, the quadrant of the terminal side, and the sine and cosine of .

Enter the exact answers.

For the number π, either choose π from the drop-down menu (under α) or type in Pi (with a capital P).

The terminal side of the angle lies in quadrant __________ .

Its reference angle is __________.

Question 5: (3 points)

A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0, 1) , that is, on the due north position. Assume the carousel revolves counterclockwise.

What are the coordinates of the child after 90 seconds?

Enter the exact answer as a point, (a, b).

__________

Question 6: (3 points)

Evaluate csc ( ).

Enter the exact answer.

csc ( ) = __________

Question 7: (3 points)

If tan t = − and < t < 2  π, find sin t, cos t , sec t, csc t, cot t.

Enter the exact answers.

sin t =

cos t =

sec t =

csc t =

cot t =

Question 8: (6 points)

Use the angle in the unit circle to find the value of the three trigonometric functions below.

Enter the exact answers.

sin t =

tan t =

sec t =

Show your work and explain, in your own words, how you arrived at your answers.

__________

Question 9: (3 points)

Use a graphing calculator to evaluate tan ( ).

Round your answer to three decimal places.

____________

Question 10: (3 points)

The equation P = 20 sin (2πt) + 110 models the blood pressure, P , where t represents time in seconds.

a. Find the blood pressure after 40 seconds.

Enter the exact answer.

The blood pressure is ____________ .

b. What are the maximum and minimum blood pressures?

Enter the exact answers.

The maximum blood pressure is ____________ , and the minimum blood pressure is ____________ .

Question 11: (6 points)

Graph two full periods of the function f (x) = cos (6x) and state the amplitude and period.

Enter the exact answers.

For the number π, either choose π from the bar at the top or type in Pi (with a capital P).

Amplitude: A = ____________

Period: P = __________

Select the correct graph of the function f (x) = cos (6x) .

(a)

(b)

(c) (d)

(e)

Show your work and explain, in your own words, how you arrived at your answers.

__________

Question 12: (3 points)

Graph one full period of the function f (x) = 4 sin ( (x − 3)) + 8 starting at x = 0, and state the amplitude, period, and midline.

State the maximum and minimum y-values and their smallest positive corresponding x-values. State the phase shift and vertical translation.

Enter the exact answers.

Amplitude: A = ____________

Period: P = __________

Midline: y = ____________

Maximum y-value and smallest positive corresponding x-value:

x = __________ y = __________

Minimum y-value and smallest positive corresponding x-value:

x = __________ y = __________

The phase shift is __________.

The vertical translation is __________.

Select the correct graph of the function f (x) = 4 sin ( (x − 3)) + 8 .

(a) (b)

(c)

(d) (e)

Question 13: (3 points)

Determine the amplitude, midline, period, and an equation involving the sine function for the graph shown below.

Enter the exact answers.

Amplitude: A = ____________

Midline: y = ____________ Period:

P =	__________

Enclose arguments of functions in parentheses. For example, sin (2 * x).

Include a multiplication sign between symbols. For example, a * π.

For the number π, either choose π from the drop-down menu (under α) or type in Pi (with a capital P).

y = __________

Question 14: (3 points)

Let f (x) = cos x. Determine the x-value(s) where the function has a maximum or minimum value on [0, 2π).

To enter π, type Pi (with a capital P).

The fields below accept a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x − 1 ). The order of the lists do not matter.

On [0, 2π), the maximum value(s) of the function occur(s) at what x-value(s)?

x = __________

On [0, 2π), the minimum value(s) of the function occur(s) at what x-value(s)?

x = __________

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