## sierraurb one year ago Trignometric functions help!!

1. sierraurb

prove $\sin \Theta -\sin \Theta \times \cos ^{2}\Theta =\sin ^{3}\Theta$ show all work

2. sierraurb

I get that you'd start by multiplying sin(theta) and cos^2(theta) but idk what that comes out to

3. cwrw238

use a substitution by the identity cos^2 theta = 1 - sin^2 theta

4. sierraurb

I have no idea what that means :( this is the one question i have no clue how to do

5. cwrw238

instead of cos^ theta write 1 - sin^ theta then simplify and you'll find you'll get sin^3 theta

6. sierraurb

But its cos^2theta

7. cwrw238

cos^2 theta = 1 - sin^2 theta is an established trig identity

8. sierraurb

Okay so how would i use that identity to solve?

9. sierraurb

should i replace cos^2 theta with 1-sin^2

10. cwrw238

sin theta - sin theta * cos^ theta = sin theta - sin theta ( 1 - sin^2 theta) now expand the brackets and simplify

11. cwrw238

yes i've replaced cos^2 theta with 1 - sin^2 theta

12. sierraurb

do i subctract the two sin theta's or distribute the one?

13. cwrw238

distribute the sin theta over the parentheses is the next step

14. cwrw238

* rather you distribute - sin theta

15. sierraurb

so its sin theta - sin theta - sin^3 theta

16. sierraurb

and the two sin theta's cancel out and leave me with sin^3 theta?

17. cwrw238

no - remember:- - times - = +

18. cwrw238

yes ( but note the sign of sin^3 theta is positive)

19. sierraurb

I understand now!! Thank you so so much I appreciate it a lot :)

20. cwrw238

- sin theta - sin^2 theta = + sin^3 theta

21. cwrw238

yw