Homework Help: Math - Solving Trig Equations

Posted by Anonymous on Wednesday, November 21, 2007 at 6:29pm.

Solve each equation for 0 is less than and equal to "x" is less than and equal to 360

3sinx = 2cos^{2}x

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I don't know how to solve this equation...this is what I have, but I don't know if I'm on the right track or not

3sinx = 1 - 2sin^{2}x
3sinx - 1 + 2sin^{2}x = 0
2sin^{2}x + 3sinx - 1 = 0
sinx(3 + 2sinx) = 1

...and if I am, what do I do next now?

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The answers are:
30 and 150 degrees

Math - Solving Trig Equations - Michael, Wednesday, November 21, 2007 at 6:35pm
3sinx = 2cos^2(x)

I believe you've treated this as cos(2x) and expanded it as a double-angle identity. However, you can't do this because the cosine function is being squared. The 2 is not being multiplied by the x.

I'm working on it...
- Math - Solving Trig Equations - Michael, Wednesday, November 21, 2007 at 6:43pm
  Start by recalling the most important identity. My math teacher calls this "the #1 Identity."
  
  sin^2(x) + cos^2(x) = 1
  
  We want to simplify our trig equation by writing everything in terms of sine. Let's solve the #1 Identity for cos^2(x) because we have that in our trig equation.
  
  cos^2(x) = 1 - sin^2(x)
  
  Plug that into the trig equation, and see what you can get from there. Let me know if you get stuck along the way.
Math - Solving Trig Equations - Anonymous, Wednesday, November 21, 2007 at 6:49pm
wow I forgot about that identity, thank you!

But, I'm still stuck...

I get
cos^2x + sin^2x = 1

I can't use any compound identities for this...I don't know how to isolate for either cos or sin...
- Math - Solving Trig Equations - Michael, Wednesday, November 21, 2007 at 6:57pm
  The only identity you need it the #1 Identity.
  
  Plugging in 1 - sin^2(x) for cos^2(x), you should get...
  
  3sinx = 2(1 - sin^2(x))
  
  Use the distributive property, collect everything on the left, and then factor.
- Math - Solving Trig Equations - Michael, Wednesday, November 21, 2007 at 6:57pm
  The only identity you need is the #1 Identity.
  
  Plugging in 1 - sin^2(x) for cos^2(x), you should get...
  
  3sinx = 2(1 - sin^2(x))
  
  Use the distributive property, collect everything on the left, and then factor.
Math - Solving Trig Equations - Anonymous, Wednesday, November 21, 2007 at 7:09pm
thanks, I solved it :)
- Math - Solving Trig Equations - Michael, Wednesday, November 21, 2007 at 7:38pm
  Glad to be of service. :)

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