Question

A sine function has an amplitude of 3, a period of pi, and a phase shift of pi/4 What is the y-intercept of the function?​

Answer 1

To find the y-intercept of a sine function with an amplitude of 3, a period of pi, and a phase shift of pi/4, substitute x = 0 into the equation and solve for y.

Step-by-step explanation:

To find the y-intercept of a sine function with an amplitude of 3, a period of pi, and a phase shift of pi/4, we need to know the general equation of a sine function: y = A sin(Bx + C) + D. In this case, the amplitude A is 3, the period is pi, and the phase shift C is pi/4. The y-intercept is the value of y when x = 0. To find it, we can substitute x = 0 into the equation: y = 3sin(pi/4) + D. Since sin(pi/4) = sqrt(2)/2, the equation becomes y = 3(sqrt(2)/2) + D. Simplifying further, we have y = (3sqrt(2))/2 + D. The y-intercept is the constant term D. Therefore, the y-intercept of this function is (3sqrt(2))/2 + D.

Answer 2

Answer: 0

Step-by-step explanation:

2pi/4 does not equal pi, it equals half of pi. 2pi/2 equals pi. Regardless here's my answer, since it also checks out for a similar function that was confirmed to have a phase shift of pi/2:

The formula for this is asin(bx - c) + d, where

|a| = amplitude

period = 2pi/b

and phase shift = c/b

The amplitude is 3

3sin(bx - c) + d

Phase shift is c/b, in this case, pi/4

3sin(4x - pi) + d

d is vertical shift

(phase shift, c, is also known as horizontal shift)

We don't see any d here so graph on Desmos as follows....

Graph 3sin(4x - pi)

Looks like the y-intercept is 0

Check by substituting 0 for x:

3sin(4x - pi)

3sin(4(0) - pi)

3sin(-pi) = 0

The answer is 0, checks out.