# Thread: Can plz you list the formulae of function change while putting ((pie/2) - x )

1. ## Can plz you list the formulae of function change while putting ((pie/2) - x )

Can plz you list the formulae of function change while putting ((pie/2) - x ) like
sin(pie/2 - x) = sin x
cos (pie/2 - x) = - sin x
something like that.

Also, explain it using graph (4 quadrant system, All +ve in 1st quad, Sin +ve in 2 quad, T in 3rd, C in 4th quad method)
Means how I use this ASTC for help in these formulae.

Thanks

2. Hello utsav
Originally Posted by utsav
Can plz you list the formulae of function change while putting ((pie/2) - x ) like
sin(pie/2 - x) = sin x
cos (pie/2 - x) = - sin x
something like that.

Also, explain it using graph (4 quadrant system, All +ve in 1st quad, Sin +ve in 2 quad, T in 3rd, C in 4th quad method)
Means how I use this ASTC for help in these formulae.

Thanks
$\displaystyle \sin(\tfrac12\pi-x) = \cos x$

$\displaystyle \cos(\tfrac12\pi-x) = \sin x$

$\displaystyle \tan(\tfrac12\pi-x) = \cot x$

$\displaystyle \cot(\tfrac12\pi-x) = \tan x$

If you reflect the graph of $\displaystyle y = \sin x$ in the line $\displaystyle x = \frac{\pi}{4}$ it becomes the graph of $\displaystyle y = \cos x$. This explains the first two formulae.

Also if you reflect the graph of $\displaystyle y = \tan x$ in the line $\displaystyle x = \frac{\pi}{4}$ it becomes the graph of $\displaystyle y = \cot x$. This explains the last two formulae.

3. 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

4. Remember it is Pi ($\displaystyle \pi$) and not Pie ()

5. Originally Posted by Bacterius
Remember it is Pi ($\displaystyle \pi$) and not Pie ( )
Oh yes, of course its Pi.

6. 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.

7. 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
sin (A+B) =sinAcosB +sinBcosA
sin (A-B) =sinAcosB-sinBcosA
cos(A+B) =cosAcosB-sinAsinB
cos(A-B) =cosAcosB+sinAsinB
tan(A+B) = (tanA+tanB)/(1-tanAtanB)
tan(A-B) = (tanA-tanB)/(1+tanAtanB)

8. 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
Study sine, cosine,and tangent graphs. It will help you in answering questions. for example sin and cos are both sinusoidal curves starting from 0 and 1 respectively.