Hello utsav Originally Posted by

**utsav** OK.

By which formula do we get **- sin x** or **- cos x**

I know a little something that All is +ve in first quadrant, only sin is +ve in 2nd quad, tan in 3rd and cos in 4th quad.

Maybe we can use this to determine +ve or -ve sin/cos when we add or subtract 2pie.

Thanks

Perhaps you're thinking of:

$\displaystyle \sin (\pi+x) = -\sin x$

$\displaystyle \cos(\pi-x) = -\cos x$

These relationships (and the ones I have you before) can be worked out in several ways:

- Using the unit circle and the four quadrants; or

- Using the graphs of $\displaystyle y = \sin x,\; y= \cos x,\; y = \tan x,\; y= \cot x$; or

- Using the addition formulae for sine and cosine; for example:

$\displaystyle \sin (A+B) = \sin A \cos B+ \cos A\sin B$, etc

and then using facts like $\displaystyle \sin\left(\frac{\pi}{2}\right) = 1,\; \sin \pi = 0$, etc.

Grandad