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\begin{center}
\textbf{Solving Trigonometric Equations - March 25, 2002}
\end{center}

\begin{itemize}
\item  Solve these all algebraically if possible (most are possible).
(You might have to use a calculator as a final step for doing an inverse trig function.)
\item  Check your work graphically with your calculator (especially for the ones you are a bit unsure of!).
\item  Practice writing your answer down with $+2k\pi$.
\end{itemize}


\begin{enumerate}

\item  $2\sin 3x -1 =0$
\\Hint: can you first get $\sin 3x$ alone?

\item  $\cot x \cos^2 x = 2\cot x$
\\Hint: can you factor anything?

\item  $2\sin^2x - \sin x -1 = 0$
\\Hint: can you factor it? (If you can't see it, try substituting $u=\sin x$).

\item  $2\cos(3x-1)=0$
\\Hint: what values of $u$ make $\cos u=0$?

\item  $\sec^2x - 2\tan x = 4$
\\Hint: Can you first make sure you only have one trig function in the equations (use an identity).

\item  \[ \frac{1+\sin x}{\cos x} + \frac{\cos x}{1+\sin x} =0 \]
Hint: can you first ``clear denominators?''

\item  $\sin 2x \sin x - \cos x = 0$
\\item  Any trig identities you can use?

\item  $\cos x + \cos^2(x/2) = 2$
\\Hint  Trig identities?

\item  $\sin x = 3 \cos x$
\\Hint: Can you make this equation have only one trig function instead of two?

\item  $2\cos^2x + \sin 2x = 0$
\\Hint: Here you have two problems: there are two different trig functions and one has an $x$ inside and the other has a $2x$.


\end{enumerate}













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