Identies: Sum And Difference, Double Angle hurry

In summary, the student was trying to solve a problem involving the equalities sin3x = (sinx)(3-4sin^2 x). They first split sin3x into sin(x+2x) and then used the sum and double angle identities to get (sinx)(1-2sin^2 x)+(2sinxcosx)(cosx). They then solved for sin(x), which resulted in the correct answer.
  • #1
emohunter7
19
0
I need some help with these kind of problems. I don't clearly understand how to solve them. Here is one...PLEASE HELP!

sin 3x = (sin x)(3-4sin^2 x) PROVE THEY ARE EQUAL
 
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  • #2
emohunter7 said:
I need some help with these kind of problems. I don't clearly understand how to solve them. Here is one...PLEASE HELP!

sin 3x = (sin x)(3-4sin^2 x) PROVE THEY ARE EQUAL

You can use identities sin(x+y) = cos(x)sin(y) + sin(x)cos(y) and sin(2x) = 2sin(x)cos(x) for this. Merely write 3x slightly differently so that the use of these identities becomes more evident.
 
  • #3
thank you...alright this one i am stuck on...i have been working on it for 10 minutes and can't come up with the answer.
2csc2x=(csc^2x)(tanx)
 
  • #4
would the correct answer for my first problem be:
change sin3x to (sinx)(sin2x)
then change sin2x to 2sinxcosx
then change that to (2sinx)(2-2sinx)
then...i don't know...but am I on the right track??
 
  • #5
emohunter7 said:
change sin3x to (sinx)(sin2x)

This is incorrect. Put sin(3x) = sin(x + 2x) instead.
 
  • #6
okay thank you I will try that
 
  • #7
alright as my next step I put (sinx)(cos2x)+(sin2x)(cosx)...is this correct?
 
  • #8
do I then change the cos's to sin's?
 
  • #9
emohunter7 said:
alright as my next step I put (sinx)(cos2x)+(sin2x)(cosx)...is this correct?

Yes. Perhaps you should attempt the entire problem and then post your solution instead of posting line by line.
 
  • #10
sorry I just need to know where I'm messing up.
 
  • #11
jostpuur said:
You can use identities sin(x+y) = cos(x)sin(y) + sin(x)cos(y) and sin(2x) = 2sin(x)cos(x) for this.

emohunter7 said:
do I then change the cos's to sin's?

Okey, my first advice wasn't flawless because I didn't notice that you need the formula for cos(2x) too. You cannot switch sines to cosines arbitrarily.
 
  • #12
so by using cos2x and sin2x formulas I should get (sinx)(1-2sin^2 x)+(2sinxcosx)(cosx)...right??
 
  • #13
emohunter7 said:
so by using cos2x and sin2x formulas I should get (sinx)(1-2sin^2 x)+(2sinxcosx)(cosx)...right??

Correct.
 
  • #14
then do I multiply the (2sinxcosx)(cosx) ?
 
  • #15
Rewrite what your problem is and what you want to solve starting from the beginning please.
 
  • #16
the problem is:
sin3x = (sinx)(3-4sin^2 x) ...PROVE THAT THEY ARE EQUAL
 
  • #17
Ok, show some work now.

(Im going to bed in 10 min, so type fast if you want help).
 
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  • #18
ok...
first i split sin3x making sin(x+2x)
than i used the sum identity making (sinx)(cos2x)+(sin2x)(cosx)
then i used double angle identity making (sinx)(1-2sin^2 x)+(2sinxcosx)(cosx)
dunno what to do next
 
  • #19
Factor out a sin(x).
 
  • #20
i got it :) thanks!
new homework... will you help me with it if I have trouble?
 
  • #21
Feel free to post your question and your work on it.
 
  • #22
okay thank you
 

1. What is the sum identity for sine and cosine?

The sum identity for sine and cosine is sin(a + b) = sin(a)cos(b) + cos(a)sin(b).

2. How can I use the sum identity to find the value of a trigonometric function?

You can use the sum identity by substituting in the values of a and b and then solving the resulting equation.

3. What is the double angle identity for tangent?

The double angle identity for tangent is tan(2a) = 2tan(a) / 1 - tan²(a).

4. How can I use the double angle identity to simplify a trigonometric expression?

You can use the double angle identity by substituting in the value of a and then simplifying the resulting expression using algebraic manipulations.

5. Can the sum and double angle identities be applied to all trigonometric functions?

Yes, the sum and double angle identities can be applied to all trigonometric functions, including sine, cosine, tangent, secant, cosecant, and cotangent.

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