Write an equation for each translation. y=sin x, π/4 units to the right
y=sin(x-π/4)
can you show your work
Sure!
To translate the graph of y=sin x by π/4 units to the right, we need to replace the "x" in the equation with "x-π/4". This will shift the entire graph horizontally by π/4 units to the right.
So our new equation is:
y = sin(x-π/4)
This means that for any given value of x, we will take that value, subtract π/4 from it, and then plug the result into the sin function to find the corresponding y-value. This will give us the same pattern as the original y=sin x graph, but shifted π/4 units to the right.
no words just a series of what you did to get your answer
Original equation: y = sin x
Translation: π/4 units to the right
Transformation: replace x with (x-π/4)
New equation: y = sin(x-π/4)
To translate the equation y = sin(x) π/4 units to the right, we need to substitute x with (x - π/4) in the equation:
y = sin(x - π/4)
To translate the function y = sin x π/4 units to the right, we need to subtract π/4 from the variable x. This will shift the entire graph to the right by π/4 units.
Therefore, the equation for the translation of y = sin x π/4 units to the right is:
y = sin(x - π/4)