Question

write an equation for each translation y=sinx, x/4 units to the right
y=sinx-pi/4)

Answer 1

There appears to be an error in the given information. If y = sin(x) is translated x/4 units to the right, the equation would be y = sin(x - pi/2).

Explanation: The standard equation for sinusoidal functions is y = A*sin(B(x - h)) + k, where A is the amplitude, B is the period (2pi/B), h is the horizontal shift, and k is the vertical shift. In this case, A = 1 since we are dealing with the basic sine function, B = 1 since the period of sin(x) is 2pi, and k = 0 since there is no vertical shift.

To find the horizontal shift, we need to look at the value of h in the equation. We know that x/4 units to the right corresponds to a horizontal shift of h = x/4. Therefore, we have:

y = sin(B(x - h)) = sin(x - (pi/2)*(x/4)) = sin(x - pi/2)

Note that pi/2 is half of the period of sin(x), which is why we multiply x/4 by pi/2 in the calculation.