1. What is the period of the function?
y = 4 cos pi x
A. 1
B. 2
C. pi
D. 2pi
2. Which represents the reference angle for 2pi/3?
A. 2pi/3
B. pi/3
C. pi/4
D. pi/6
the period of cos(kx) is 2pi/k
So, cos(pi x) has period 2
#2 pi/3
Yis
1. To find the period of the function y = 4 cos(pi x), you need to understand that the period of a cosine function is given by the formula T = 2pi/b, where b is the coefficient of x. In this case, the coefficient of x is pi. So, the period is calculated as T = 2pi/pi = 2. Therefore, the correct answer is B. 2.
2. To find the reference angle for 2pi/3, you need to understand that the reference angle is the positive acute angle between the terminal side of the angle and the x-axis in standard position. In this case, the angle 2pi/3 lies in the second quadrant, where cosine is negative. To determine the reference angle, subtract 2pi/3 from pi. pi - 2pi/3 = 3pi/3 - 2pi/3 = pi/3. Therefore, the correct answer is B. pi/3.