Question

Trignometric functions help!!

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

instead of cos^ theta write 1 - sin^ theta

then simplify and you'll find you'll get sin^3 theta

Answer 6

But its cos^2theta

Answer 7

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

Answer 8

Okay so how would i use that identity to solve?

Answer 9

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

Answer 10

sin theta - sin theta * cos^ theta
= sin theta - sin theta ( 1 - sin^2 theta)

now expand the brackets and simplify

Answer 11

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

Answer 12

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

Answer 13

distribute the sin theta over the parentheses is the next step

Answer 14

* rather you distribute - sin theta

Answer 15

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

Answer 16

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

Answer 17

no - remember:- - times - = +

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

yw