Question

Sin ( x - 11π) = ?

Answer 1

`sin(x-11pi)=-sinx`

Explanation:

Adding `2pi` or its multiple to an angle, does not change value of its trigonometric ratio.

Hence `sinA=sin(A+2pi)=sin(A+4pi)=sin(A+6pi)=........`

similarly `cosA=cos(A+2pi)=cos(A+4pi)=cos(A+6pi)=........`,

`tanA=tan(A+2pi)=tan(A+4pi)=tan(A+6pi)=........` and so on for all trigonometric ratios

Hence `sin(x-11pi)=sin(x-11pi+12pi)=sin(pi+x)` - note that `12pi=2pixx6`

Now as `sin(pi+A)=-sinA`

Hence `sin(x-11pi)=sin(pi+x)=-sinx`