Michael Fremista: Solving Trigonometric Equation

Michael R. Fremista
IV - Emerald

Life is like a Math. You are supposed to find a way for you to escape and survive in all the struggles that keep on coming in your life. Not always in the time that you are in the peak of success, because life is like a roller coaster that keeps on navigating and rolling in your own circle.

Solving Trigonometric Equation is not a piece of cake for me. But first, what is Trigonometric Equation?
It's an equation that involves some trigonometric functions of the variable.

RULES for solving algebraic equations also applies in solving trigonometric equations.
1. Adding the same expression to both members of an equation produces an equivalent equation.
2. Multiplying each member of an equation by the same expression (nonzero real number) produces an equivalent equation.
3. Replacing any expression in an equation by another expression representing the same real number produces an equivalent equation.

For example, $2sin\left( x\right) -1=0$
There are an infinite number of solutions to this problem. To solve for x, you must first isolate the sine term.

$\begin{eqnarray*}&& \\ 2\sin \left( x\right) -1 &=&0 \\ && \\ \sin \left( x\right) &=&\displaystyle \frac{1}{2} \\ && \\ && \end{eqnarray*}$

Solution Set:

We know that the $\sin \left( \displaystyle \frac{\pi }{6}\right) =\displaystyle \frac{1}{2},$ therefore $x=\displaystyle \frac{\pi }{6}.$ The sine function is positive in quadrants I and II. The $\sin \left( \pi -\displaystyle \frac{\pi }{6}\right) =\sin \displaystyle \frac{5\pi }{6}$ is also equal to $\displaystyle \frac{1}{2}.$ Therefore, two of the solutions to the problem are

$x=\displaystyle \frac{\pi }{6}$ and $x=\displaystyle \frac{5\pi }{6}.$

Sometimes, the hardest thing has a mystery solution. Just like in reality, you need to find a key to prove into yourself that you're not a weak that you have a power and strength to show to others. In this topic, the only ingredient or key to solve the equation is having a patience in yourself and having analyzation skills.

Michael Fremista

Saturday, December 13, 2014

Solving Trigonometric Equation

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