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

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?

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 doubleangle 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  Elvis, Sunday, January 10, 2016 at 6:33pm
Is d answer 90degree
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