Math CentralQuandaries & Queries


Question from Yamama:

hello ! I need help to solve this equation :

2cos^2 x + sin x = 2

Thank you very much

Hi Yamama,

Write the equation as

\[2cos^2 x + sin x -2 = 0\]

and use the fact that

\[\sin^2(x) + \cos^2(x) = 1\]

to express your equation as a quadratic in $\sin(x).$ Solve the quadratic.

If you have an app on your computer that will graph equations you can use it to plot the graph of

\[y = 2cos^2 x + sin x -2 \]

to verify that you have found all the solutions.


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