3.1-3.3 Quiz

The amplitude of a periodic function is 3.5 units and the minimum value of the function is 2. What is the maximum value of the function?

• 3.5

• 5.5

• 7

• 9

A periodic functions goes through 15 cycles in 7 minutes. What is the period of one cycle?

• 33 seconds

• 30 seconds

• 28 seconds

• 21 seconds

For the periodic function, a portion of the graph is shown below. Given that f(−2) = 3, find the value of the period, k. It is known, for any integer value of n, that f(x + nk) = f(−2). What is the ordered pair on the graph of f when n = 2?

• k = 12; f(10) = 3

• k = 16; f(30) = 3

• k = 16; f(34) = −2

• k = 12; f(−26) = 3

Find the point (x,y) on the unit circle that corresponds to the real number t = (17π/6).

• ( -√3/2 , 1/2 )

• ( √3/2 , -1/2 )

• ( √3/2 , 1/2 )

• ( -1/2 , √3/2 )

The figure shows a circle centered at the origin with an angle of measure θ radians in standard position. The coordinates of P are (-x,y) where the terminal ray of the angle intersects the circle. Which of the following statements is true about the cosine of θ?

• cos θ = y/3, because it is the ratio of the vertical displacement of P from the y-axis to the distance between the origin and P

• cos θ = -y/3, because it is the ratio of the vertical displacement of P from the y-axis to the distance between the origin and P

• cos θ = -x/3, because it is the ratio of the horizontal displacement of P from the y-axis to the distance between the origin and P.

• cos θ = x/3, because it is the ratio of the horizontal displacement of P from the y-axis to the distance between the origin and P.

If sin θ < 0 and cos θ = -2/5, find tangent of θ and the coordinates of point P = (x,y)

• tan θ = -√21/5; P = (5, -√21)

• tan θ = √21/2; P = (-2, -√21)

• tan θ = √29/2; P = (-2, -√29)

• tan θ = 2/√21; P = (-√21, -2)

State the amplitude, period, and midline for y = g(x). Use the graph to analyze the function and complete the following question.

• amplitude: 8 period: 6 midline: y = 1

• amplitude: 5 period: 12 midline: y = 1

• amplitude: 4 period: 12 midline: y = 1

• amplitude: 8 Period: 6 midline: y = 2

For any integer value, n, state the intervals where the graph of y = g(x) is concave up. Use the graph to analyze the function and complete the following question.

• (0 + 12n, 6 + 12n)

• (−6 + 12n, 0 + 12n)

• (0 + 6n, 6 + 6n)

• (−6 + 6n, 0 + 6n)

For any integer value, n, state the intervals of decrease. Use the graph to analyze the function and complete the following question.

• [3 + 12n, 9 + 12n]

• [5 + 12n, −3 + 12n]

• [−3 + 6n, 0 + 6n]

• [3 + 6n, 9 + 6n]

If cos θ = -7/8 and π ≤ θ ≤ 3π/2, find tan θ

• 7/√15

• 7√15/15

• √15/7

• -7√113/113