## mathslover 4 years ago sin ( 90 + theta ) = cos theta prove^

1. anonymous

i guess it depends on what you can use if you can use the addition angle formula, that would work if not maybe with a triangle you can see it

2. mathslover

i want to do with the triangle one but m wondering how will you show (90+theta) in a right angled triangle?

3. anonymous

|dw:1350098235823:dw|

4. mathslover

yes but that is 90 - theta? do 90-theta has any relation with 90 + theta ?

5. anonymous

$\cos(x)=\frac{a}{c}=\sin(90-x)=-\sin(x-90)$ $=\sin(x-90+180)=\sin(x+90)$

6. mathslover

how : -sin(x-90) = sin(x-90+180) ?

7. anonymous

third equal sign because sine is odd, fourth because $$\sin(x)=-\sin(x+180)$$

8. mathslover

Gotcha now, thanks a lot!

9. anonymous

your on the other side of the unit circle |dw:1350098472701:dw|

10. anonymous

yw

11. mathslover

hey, how you did this step? : $\large{-\sin(x-90) = sin(x-90+180) }$ ?

12. mathslover

@satellite73 did you subtract sin(180) both sides?

13. anonymous

i added 180 inside because $$\sin(x)=-\sin(x+180)$$

14. mathslover

oh k , got it!