A math problem with graphs?

Question

Im totally lost with this problem....


What transformation could be used to make the graph of the equation y=sin x coincide with the graph of the equation y=cos x ?

Translation

Rotation

Dilation

Point Reflection


Thanks!!!

Answer 1

Easy: just look at the graphs of sin x and cos x
At x = 0, sin x = 0 and cos x = 1
If you were to translate x + 90 of x, then at x = 0 sin 90 = 1 which coincides with cos 0 = 1.
SOOOO...the answer is translation, specifically
sin (x + pi/2) = cos x

Answer 2

The easiest way might be to shift (translate) left or right.

The graphs of y=sinx and y=cosx are similar, and appear different in that one is offset from the other pi/2 radians or 90* (left or right).

That is to say, if you shifted one of the two graphs 90* left, or right it would 'match-up' with the other.

think: (for a Cartesian 2D graph)

translation= left or right, up or down (shape stays the same)
rotation= rotates (shape stays the same)
dilation= shape changes
point reflection= mirror image

Shifting the graph represented by y=sinx, left or right, pi/2 radians, or 90* if you prefer, would make it coincide with the graph of y=cosx
y=sin(x+/-90*) = cosx

Actually y=sin[x + (k)90*] where k is any odd numbered integer should look the same as y=cosx , I think! Been too long!

n.b. It helps so much knowing how to work trig functions within the UNIT CIRCLE! Then there is no guessing and little memorizing required!!

Answer 3

Translation---yes, shift Sin(x) to the right or left until it matches Cos(x)

Rotation---yes, rotate the function Sin(x) 180 degrees about the point x = (3/4)π, for example.

Dilation---no

Point Reflection---yes, any line drawn through the point x = (3/4)π, for example, will intersect both Sin(x) and Cos(x) at equal distances from the point.

Note that in 2 dimensions, a point reflection is the same as a rotation of 180 degrees.

Note 2: A point reflection isn't the same as an mirror image.

Answer 4

just shove the whole thing along the x axix

ie translation