First Principles AI

Question 1

Draw the graph of each of the following function for the intervals mentioned against each:

$y = -\sin 2x$ , $x \in [-2\pi, 2\pi]$

$y = 2\cos 2x$ , $x \in [-2\pi, 2\pi]$

$y = \tan 2x$ , $x \in [-\pi, \pi]$

$y = \tan \dfrac{x}{2}$ , $x \in [-2\pi, 2\pi]$

$y = \sin \dfrac{\pi}{2}x$ , $x \in [0, 2\pi]$

$y = \cos \dfrac{\pi}{2}x$ , $x \in [-\pi, \pi]$

Question 2

On the same axes and to the same scale, draw the graphs of the following functions for their complete period:

$y = \sin x$ and $y = \sin 2x$

$y = \cos x$ and $y = \cos 2x$

Question 3

Solve graphically:

$\sin x = \cos x$ , $x \in [0, \pi]$

$\sin x = x$ , $x \in [0, \pi]$

Questions