trigonmentry Math

Question

Answer the following parts of the question:

1. Sketch a graph of y=cos x.
2. By translating, sketch a graph of y=cos (x+π)
3. By reflecting the graph of part (a), sketch a graph of y= -cos x.
4. How do the graphs of parts (b) and (c) compare?

Answer 1

cosx transformed to cos(x+pi) is a horizontal shift left by pi or a leftward shift by pi

or a rightward shift by pi

or a right or leftward horizontal shift by 2npi+pi where n= any integer

or a shift of pi(2n+1) left or right

a reflection across the y axis would mean cosx = -cosx, changing nothing, not changing anything, all points on the graph identical before and after the reflection

it's an even function, a mirror image if a mirror were placed at the y axis