Question

Part 1: Using complete sentences, compare the key features and graphs of sine and cosine. What are their similarities and differences?

Part 2: Using these similarities and differences, how would you transform f(x) = 4 sin(2x - π) + 3 into a cosine function in the form f(x) = a cos(bx - c) + d?

Answer 1

The relationship between the cosine and sine graphs is that the cosine is the same as the sine — only it’s shifted to the left by 90 degrees, or π/2. The graph of the cosine is the darker curve; note how it’s shifted to the left of the sine curve.
The graphs of y = sin x and y = cos x on the same axes.
The graphs of the sine and cosine functions illustrate a property that exists for several pairings of the different trig functions. The property represented here is based on the right triangle and the two acute or complementary angles in a right triangle. The identities that arise from the triangle are called the cofunction identities.

More information found on: http://www.dummies.com/how-to/content/comparing-cosine-and-sine-functions-in-a-graph.html