Sinusoidal means looking like a basic sine graph. By how many degrees do you have to shift sin x = y to the right to make it look like the graph of cos x = y? (Enter only the number of degrees.)
90
Select all the true statements about the graphs of these two functions.
•h(x) = sin (x + ð/4)
•h(x) = cos (x - ð/4)
Ans:The sine function is shifted to the left by ð/4, while the cosine function is shifted to the right by ð/4.
The graphs of these two functions coincide.
correct
21
To shift the graph of sin(x) to make it look like the graph of cos(x), we need to determine the phase shift between the two functions. The difference between the two graphs lies in their phase, which represents how far the graph is shifted horizontally (to the left or right).
The general equation for a sinusoidal function is given by:
y = A * sin(B * (x - C)) + D
In this case, for sin(x) = y, A = 1, B = 1, C = 0, and D = 0. And for cos(x) = y, A = 1, B = 1, C = ? (unknown horizontal shift), and D = 0.
To find the difference in phase, we need to analyze the value of "C" for cos(x) = y. By comparing the two equations, we know that C represents the horizontal shift. Since C = 0 for sin(x) = y, we need to find the value of C for cos(x) = y to determine the shift.
The cosine function is a shift of the sine function by π/2 radians (or 90 degrees). Therefore, we can conclude that to shift sin(x) to make it look like cos(x), we need to shift it by π/2 radians or 90 degrees to the right.
So, the answer is 90 degrees.