Question

How are the intervals similar where the graphs of y = sin(x) and y = cos(x) are increasing and where the graphs for y = sin(x) and y = cos(x) are decreasing? How are they different?

a) They have the same intervals of increase and decrease.
b) They have different intervals of increase and decrease.
c) They both only have increasing intervals.
d) They both only have decreasing intervals.

Answer 1

The graphs of y = sin(x) and y = cos(x) have the same intervals of increase and decrease, but may have a phase shift.

Step-by-step explanation:

The graphs of y = sin(x) and y = cos(x) have the same intervals of increase and decrease. Both graphs increase from 0 to π/2, then decrease from π/2 to π, and so on. The only difference is the phase shift between the two graphs, meaning that one graph is shifted to the right or left compared to the other graph.

So the correct answer is a) They have the same intervals of increase and decrease.