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.