Question

From the curve y = sin x, graph the functions 

(i) y = sin(-x) 

(ii) y = -sin(-x) 

(iii) y = sin((π/2) + x) which is cos x 

(iv) y = sin((π/2) – x) which is also cos x (refer trigonometry)

Answer 1

First we have to draw the curve y = sin x

(i) y = sin(-x) = – sin x = f(x)

(ii) y = -sin(-x) = -[-sin x] = sin x

It is the same as y = sin x by shifting the graph to (π/2) to the left.

(iii) y = sin((π/2) + x) is the graph which is obtained from y = sin x by shifting the graph to (π/2) to the left. 

(iv) y = sin((π/2) - x) is the graph obtained from y = sin x by shifting the graph to (π/2) to the right.