Comparison of the sine and cosine graphs on one set of axes.

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Comparison of the sine and cosine graphs on one set of axes. (i) Draw a neat sketch of the graphs of

y=\sin x

and

y=\cos x

for

0\le x\le2\pi

, marking all intercepts and extreme points. (ii) By inspecting the sketch, list the approximate

x

-coordinates where the two graphs intersect in the given interval. (iii) Verify algebraically that the exact

x

-coordinates of the intersection points are

x=\dfrac{\pi}{4}+n\pi

, where

n

is an integer. Show each step clearly.