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anonymous
 one year ago
Emergency help on an Algebra II exam!
Prove: sin θ  sin θ•cos2 θ = sin3 θ. You must show all work.
anonymous
 one year ago
Emergency help on an Algebra II exam! Prove: sin θ  sin θ•cos2 θ = sin3 θ. You must show all work.

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nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1it looks like this is an exam

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's a practice exam, but it's worth a good bit of points and while I can understand the proofs written out in my lessons, this particular problem is stumping me. I've been working on these tests for hours :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I know that identity of sin^2theta + cos^2theta = 1, or...something pretty close to that...

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1show me the attempts you have made.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. So the sin theta should cancel, right? cos^2 theta = sin^3 theta ****(that 3 is a cube, not sin(3))**** I don't know what to do with that!

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1how does it cancel?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Bc it's just subtracted. Like 1  1 = 0.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sin theta  sin theta = 0.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1sin is multiplied to cos sin θ  (sin θ•cos2 θ) = sin3 θ ORDERS of operation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Parentheses first, then

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1btw, is that \(cos^2 \theta \) or \(cos (2 \theta) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The first, it's squared.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so...then do we distribute the negative into the parentheses??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm thinking maybe we subtract sin theta from both sides to give us (sin theta * cos^2 theta) = sin^2 theta

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1is that \(sin^3 \theta \) or \(sin (3 \theta) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cubed, the first one.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1you need to start typing these things appropriately because they mean different things

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry, I didn't realize it before I posted bc I just copy and pasted it to preserve the theta symbols :(

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1like this? PROVE \(sin ~\theta  (sin~ \theta ~cos^2 \theta) = sin^3 \theta \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0There weren't any parentheses, but otherwise, yes.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1so tell me what should be the best identity we can use?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The only one I know of is the one I typed above, the sin^2 theta + cos^2 theta = 1.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We didn't focus a lot on identities, so I suppose I may be forgetting some, but they aren't in my notes =/

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1what did you focus on?

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1let us use trigonometric expansion and make use of some algebra techniques like factoring, yes?

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1do you think you can factor the lefthandside (LHS) of the equation for me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry! Lost connection!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I can tryyy, hold on

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440734256689:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sin theta(1  cos^2 theta) = sin^3 theta

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1we can skip writing the theta for now and just add it in the end so it is easier, agreed?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay! sin(1  cos^2) = sin^3

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1do you have a note for your pythagorean identities? if not it is very simple \(\large sin^2 + cos^2 = 1 \) keep in mind for future reference that \(sin = y\) and \(cos = x \)

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440734748047:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep, I remember that part from the unit circle section we just did.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1you probably already learned the Pythagorean Theorem which states that the length of the longest leg \(\large r \) is equal to the square root of the sum of the two shorter legs dw:1440734959343:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1do you think we can manipulate our identity algebraically so it would look familiar as the problem you have?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y(1  x^2) = y^3 when you say cos = x and sin = y...

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440735114209:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry this is taking me so long to understand ._.

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440735291067:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440735446837:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1what part did I lose you?

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440735591245:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where did the sin^3 go?

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1that's just the lefthandside (LHS) since the board is too small for me to fit everything in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it's 1^2 + sin^3 on the right hand?

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1no, the righthandside stays the same since it is what we're trying to accomplish

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0...so then where is the sin^3 if you said it's not on the left hand? D:

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1what we are basically doing is trying to manipulate and rearrange the lefthandside of your problem so it would EQUAL to the righthand side of the problem

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440735790511:dw

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440735817436:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, I'm mostly following

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1from the pythagorean identity, we derived that \(1cos^2 = sin^2 \) because from our original identity (derived from the unit circle) \(sin^2 + cos^2 = 1 \) we can rearrange it to \(sin^2 + cos^2 \color{red}{cos^2} =1 \color{red}{cos^2}\) simplifying to: \(sin^2 = 1cos^2 \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think any of this is getting through anymore, it's really late here and I'm thinking my exam has probably timed out by now ._. I'm tracking but I don't see where this is actually leading, we keep ending up back at this identity and I'm not sure what to do with it

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1then it would suffice to say that \(sin  sin~cos^2 = sin^3 \) because \(sin (1cos^2) = sin^3 \) because the lefthand side is equivalent to \(sin (sin^2) \) therefore \(sin^3 = sin^3 \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'll definitely reference this when I retake. Thank you so so so much for all of your time and help <3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You were very patient, I hope it comes back to you tenfold :x

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1you're not even telling me what part you are not following

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1up to what part you are able to grasp and what part seems a little fuzzy still

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry, it's just because I don't really know where I'm lost, I'm just really tired >.<

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1come back when your brain is fully rested. there is no point in studying when your brain is not working to its potential.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Exactly :( I hope you have a good night, thanks so much for the guidance, I'm sure it'l help a lot more in the morning
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