Math CentralQuandaries & Queries


Question from Jennifer, a student:

how do you solve for X? im frustrated i've forgotten how to solve this equation.

We have two responses for you

Hi Jennifer,

Use the fact that cos(2X) = 2 sin(X) cos(X).



Hi Jennifer. There are analytical ways to solve the question, using trig identities. However, an easier geomoetric solution would be to create a right angle triangle and identify one angle as X and the other as 2X. See this diagram:


So the sin X = a/h and the cos 2X = a/h. Thus sin X = cos 2X. Since all triangles have angles adding to 180 degrees, you can quickly solve for X in the equation 90 + X + 2X = 180.

This may not be the ONLY angle however. What happens if X is negative?

Stephen La Rocqu

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