Question

how to draw y=x^2 graph i know how the shape looks like but how to know y=sinx graph looks like

Answer 1

is there formula and shapes for them cause in my text book it doesnt explain

Answer 2

first, know its period.. it repeats every "pi"

so, then find its intercepts with X and y axes

then use first derivative to know its peaks and increasing and decreasing natures.

DONE

Answer 3

first derivative gives you the nature .. increasing, decreasing or an extrema

Answer 4

can u do an example if u dont mind

Answer 5

yes. take y=sin(x)
1. we know it repeats every "pi"
2. so, I'll limit myself to 0<=x<=pi

Answer 6

correction, period is "2*pi"

Answer 7

3. y-intercept. when x=0, y=0... so, passes through origin
4. x-intercept, when y=0, x=0, pi,2*pi,3*pi... n*pi
where n is any integer

Answer 8

5. what happens to y when 0<=x<=pi

we know sin(x) can never go beyond 1 and this happens for x=pi/2
and from step 3, we know it starts at (0,0)
so, we conclude, it increases continuously from 0 to pi/2

6. now, it cannot go any higher and must start coming down to "0" at x="pi" (step 4)