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, 
There are an infinite number of solutions to this problem. To solve for x, you must first isolate the sine term.

Solution Set: 

We know that the therefore  The sine function is positive in quadrants I and II. The is also equal to  Therefore, two of the solutions to the problem are

  and 

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. 

Reference Angle

Michael R. Fremista

IV - Emerald

We've just completed the half semester in this school year. We are about to face another chapter which is the start of 3rd Quarter. Trigonometry is not easy when you're not listening and giving attention to the steps that are hard to follow. One of the easiest topic that I learned is the Reference Angle. What usually comes to your mind when you heard the word 'reference'?  Isn't the source of information which is to connect into another object? Yes exactly! A reference angle is an angle formed by the x axis and the terminal side. For any given angle we need to see the angle formed by its terminal side with axis to find the reference angle. You can see all the reference angles possible for each quadrant, as each co terminal angle will be having same reference angle.

                                             
How to find Reference Angle?
Step 1 :  

Find in which quadrant the given angle belongs to.

Step 2 :  

If angle A  is in first quadrant then the reference angle will be A it self.

If angle A  is in second quadrant then the reference angle will be 180 - A .

If angle A  is in third quadrant then the reference angle will be A - 180 .

If angle A  is in fourth quadrant then the reference angle will be 360 - A.

Examples:

1. Find the reference angle to the angle 110 degrees.

   
   Step 1 :  
   Angle 110 degrees will be falling in second quadrant.
   
   
   Step 2 :  
   If angle A  is in second quadrant then the reference angle will be 180 - A .
   
   
   So 180 - 110 = 70 degrees is the reference angle.
   
   
   Answer  :  70 degrees

                                                 

1. 2. Find the reference angle to the angle 30 degrees.

   
   Step 1 :  
   Angle 30 degrees will be falling in first quadrant.
   
   
   Step 2 :  
   If angle A  is in first quadrant then the reference angle will be A it self.
   
   
   So the reference angle also 30 degrees.
   
   
   Answer  :  30 degrees 
   
   
   

                                                   

This is not hard as you thought.

You just need to follow the steps, which is the number rule in Mathematics. When you committed mistake and that's the only proof that you're not a good listener and follower.

In our life, listening can keep problems from Escalating. It is not accident that we have one mouth and two ears. When we fail to listen, we shut off much of our learning potential. Don't give up, every morning is a brand new day that God keeps on reminding to us. He is the leader that have two ears and ready to listen in our circumstances in life.  We are going to learn, we must do it by listening.