Mathematics

Problem

The graphs of

y=\sin x

and

y=\tan x

intersect at points where

\sin x=\tan x

. a. (i) Transform the equation

\sin x=\tan x

into an equivalent equation that is easier to solve. b. (ii) Solve the transformed equation for all solutions in the interval

-\pi<x<\pi

. c. (iii) Using the periodicity of the trigonometric functions involved, write the general solution of

\sin x=\tan x

for all real

x

. d. (iv) Explain, with reference to the periodicity and key features of the two graphs, why the intersection points found in part (iii) repeat at regular intervals along the

x

-axis.

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