How Do Trigonometric Functions Change with Shifts of π/2 and 2π?

[utsav55]

Homework Statement

Can you please list the formulae of function change while putting (pie/2 - x) and adding or subtracting 2Pie
basically, I need help on 2 formulae. One is add/subtract Pie/2 and the other is add/subtract 2Pie.

Homework Equations

sin (pie/2 - x) = sin x
cos (pie/2 - x) = - sin x

sin (2Pie - x) = -cos x

something like that... Its just example, may not be correct.

The Attempt at a Solution

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 or Pie.

 

[calum]

2pi equals 360 degrees and pi/2 is 90 degrees. A sine and cosine function will be the same value if you add or take away 2pi as it is the same as adding or taking away 360 degrees and since the functions repeate every 360 degrees there will be no difference.
But be aware if the value inside the brackets goes lower than 0 your answer will be negative.

Taking away or adding pi/2 is simply changing a cos function into a sin function or vice versa. So cos(x- pi/2) = sinx

Since the sin and cosine functions are very similar, they are just offset by 90 degrees (pi/2) you are just swapping them round.

 

[sumit_anand86]

please,send the formulae list of differentiation as well as integration on my email-id(sumit.anandd786@gmail.com).

 

[Mark44]

But be aware if the value inside the brackets goes lower than 0 your answer will be negative.

This isn't true. For example, cos(x - 2pi) = cos(x), for all real values of x.