write an equation for each translation y=sin x,pi/4 units to the right
y = sin(x - pi/4)
write an equation for each translation y=sinx,pi/4 units to the right please explain
The equation y = sin(x) represents the graph of the function y = sin(x) without any translations applied to it.
To translate the graph pi/4 units to the right, we need to shift every point on the graph to the right by pi/4 units. This means that the x-coordinate of every point should be increased by pi/4.
This can be accomplished by replacing the x in the equation y = sin(x) with (x - pi/4), since (x - pi/4) represents the new shifted value of x after increasing it by pi/4.
Therefore, the equation for the translation of y=sin(x), pi/4 units to the right is:
y = sin(x - pi/4)
To translate the function y = sin(x) to the right by π/4 units, you can use the equation y = sin(x - π/4).
Explanation:
When you have a function y = f(x), shifting it to the right by c units is equivalent to replacing x with (x - c) in the equation. In this case, c is π/4, so we replace x with (x - π/4) in the equation y = sin(x).
Therefore, the equation for the translation of y = sin(x), π/4 units to the right, is y = sin(x - π/4).