how to find reference angle

In our previous lesson we learned all about Reference Triangles and the power of SOH-CAH-TOA, and we briefly mentioned this idea of a Reference Angle.

Well, in this lesson we dig deeper and talk all about Reference Angles and also Reciprocal Trig Functions.

jenn explaining how to find reference angles

What is a Reference Angle, you ask?

Well, let's just say they're absolutely incredible!

Angles that have the same reference angles always have the same trigonometric function values!

Meaning the SIN, COS and TAN are all the same.

Now, the sign of the function value is positive or negative depending on the quadrant of the terminal side, but the numerical value of the trig function is the same!

A reference angle is a positive, acute angle determined by the x-axis and the terminal side of a given angle.

In other words, it's always found inside our Reference Triangle, close to the origin, in between the x-axis and the terminal side.

That's great, but why should we care?

Right Triangles and Trigonometric Functions

Finding the Function Values of an Angle

Instead of having to memorize, or use a calculator, for each and every angle in the universe…remember there are an infinite number of coterminal angles out there…. All we have to do is memorize the trigonometric functions of angles less than 90 degrees!

And, as nicely stated by Math Open Reference, this allows us to make connections between other angles and enables us to solve trigonometric equations easily.

With the power of Reference Angles and Reference Triangles at our fingertips, we are now able to fully handle all six trigonometric functions!

Wait, there are six trig functions?

Yep!

We know the basic functions already. I refer to them as the Big Three – Sine, Cosine, and Tangent. Now we introduce their reciprocals, Cosecant, Secant, and Cotangent!

We will discover that once we have the basic functions from SOH-CAH-TOA, all we have to do is flip these functions and we get three more (i.e., the reciprocal functions).

But why do we need reciprocal functions, when we already have the three fundamental ratios already?

Well, you're right.

The reciprocal trig functions are harder to calculate on their own, and you don't even find their buttons as easily on your calculator. But they are useful little ratios when we need to prove trig identities or relate one trig function to another, as stated by Algebra Lab.

Ahh, things to look forward to!

So, in this lesson we will explore and find the measure of Reference Angles and understand the three Reciprocal Trig Functions.

Reference Angles – Video

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reference angles in trig with calcworkshop