anonymous
  • anonymous
Trignometric functions help!!
Trigonometry
schrodinger
  • schrodinger
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anonymous
  • anonymous
prove \[\sin \Theta -\sin \Theta \times \cos ^{2}\Theta =\sin ^{3}\Theta \] show all work
anonymous
  • anonymous
I get that you'd start by multiplying sin(theta) and cos^2(theta) but idk what that comes out to
cwrw238
  • cwrw238
use a substitution by the identity cos^2 theta = 1 - sin^2 theta

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anonymous
  • anonymous
I have no idea what that means :( this is the one question i have no clue how to do
cwrw238
  • cwrw238
instead of cos^ theta write 1 - sin^ theta then simplify and you'll find you'll get sin^3 theta
anonymous
  • anonymous
But its cos^2theta
cwrw238
  • cwrw238
cos^2 theta = 1 - sin^2 theta is an established trig identity
anonymous
  • anonymous
Okay so how would i use that identity to solve?
anonymous
  • anonymous
should i replace cos^2 theta with 1-sin^2
cwrw238
  • cwrw238
sin theta - sin theta * cos^ theta = sin theta - sin theta ( 1 - sin^2 theta) now expand the brackets and simplify
cwrw238
  • cwrw238
yes i've replaced cos^2 theta with 1 - sin^2 theta
anonymous
  • anonymous
do i subctract the two sin theta's or distribute the one?
cwrw238
  • cwrw238
distribute the sin theta over the parentheses is the next step
cwrw238
  • cwrw238
* rather you distribute - sin theta
anonymous
  • anonymous
so its sin theta - sin theta - sin^3 theta
anonymous
  • anonymous
and the two sin theta's cancel out and leave me with sin^3 theta?
cwrw238
  • cwrw238
no - remember:- - times - = +
cwrw238
  • cwrw238
yes ( but note the sign of sin^3 theta is positive)
anonymous
  • anonymous
I understand now!! Thank you so so much I appreciate it a lot :)
cwrw238
  • cwrw238
- sin theta - sin^2 theta = + sin^3 theta
cwrw238
  • cwrw238
yw

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