Precalculus Chapter 4 Practice Exam

​ Arrange the equations into the correct column.

Groups:

(a) Produces Graph

,

(b) Does Not Produce

• y=sin(x+pi/2)

• y=-sin(x-pi/2)

• y=cosx

• y=cos(-x)

• y=sin(x-pi/2)

• y=-cosx

Find the tan(w)

• 0.4

• -0.9

• -0.9/0.4

• 0.4/-0.9

• True
• False

Choose the quadrant that best answers the question.

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Type your final answer in the simplest radical form (i.e. If the final answer is the square root of 2, type in the square root of 2 instead of a decimal approximation).

Mathematical Equivalence

ON

Answer explanation

Note that this is not the Unit circle (its radius is 3). Therefore, all our distances are tripled. Since Point C is at 60 degrees, its height from the x-axis is square root of 3 over 2. This is the same height to get DOWN to point D which is located at 300 degrees. Therefore the total distance from Point C to Point D would be 2 copies of the square root of 3...but remember this is not the Unit circle, but 3 times its size. This explains why our final answer should be 3 times the square root of 3!

Match each trig function with its correct value.

• 1/2

• cos(7pi/6)

• -1

• cos(-pi/3)

• -sqrt(3)/2

• sin(15pi/2)

• 1

• tan(5pi/4)

Find the length of the arc made from Point M to Point S, in terms of pi.

Mathematical Equivalence

ON

Answer explanation

We get the answer by remembering how radians are defined. We know that 7pi/15 radians means 7pi/15 copies of the circle's radius are wrapped around the circle at the given angle. Therefore, its length is 7pi/15 times 6 which is where 42pi/15 comes from.

Mark the right combination of values for g and h.

• g=-0.5, h=6

• g=0.5, h=6

• g=6, h=0.5

• g=-6, h=-0.5

Answer explanation

The amplitude is 0.5 since the distance from the max to the midline is 0.5. If you start at the origin, it is easy to see the graph completes one cycle after pi/3. Thus the period is pi/3. It follows that since the period for a sine graph is normally 2pi, the value of b in the equation has to be 6 since 2pi divided by 6 is pi/3.

What is the maximum value of j, the height of Point A (in feet)?

• 0

• -3.5

• 3.5

• 7

What is the midline of the graph of j?

• 0

• -3.5

• 3.5

• 7