How to solve a trigonometric equation
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How to solve a trigonometric equation

[From: ] [author: ] [Date: 12-07-11] [Hit: ]
3sin²(X)= cos²(X)?And the constraints are 0 ≤ X-Divide through by cos^2(x).The trick to those problems is to use identities and algebra to get all of the trig functions down to one reference, and then use an inverse trig function to get the answer. This isnt always possible.=> tan(X) = 1/(3)^.......
I can't remember how to do these types of problems.
For example, how would I do
3sin²(X)= cos²(X)?
And the constraints are 0 ≤ X< 2pie

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Divide through by cos^2(x).
3 tan^2(x) = 1
x = arctan(sqrt(1/3))

The trick to those problems is to use identities and algebra to get all of the trig functions down to one reference, and then use an inverse trig function to get the answer. This isn't always possible.

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see 3 sin^2(x) = cos^2(x) means that

sin^2(X) = 1
______ __
cos^2(x) 3

=> tan^2(x) = 1
--
3

=> tan(X) = 1/(3)^.5

thus X= 60 degrees or 240 degrees

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3sin^2 x = cos^2 x
3( 1 - cos^2 x ) = cos^2 x
3cos^2 x + cos^2 x- 3 = 0
1
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