Wouldn’t it be great if everyone had a buddy?
Well, in trigonometry that’s exactly what we find!
A Cofunction is just math’s way of saying, “hey, these two trig functions are complements of each other and, therefore, are considered buddies.”
Wait a minute, what’s a complement?
Complementary angles are two positive angles whose sum is 90 degrees.
So?
Well, in any triangle, we know the sum of the interior angles equals 180 degrees. In a right triangle, one of the angles is 90 degrees, therefore there’s 90 degrees left between the other two angles. So, the sum of the other two angles must equal 90 degrees – so we say these two angles must be complementary!
But the excitement doesn’t end there!
Did you know that because of these two complementary angles we can prove that Sine and Cosine are buddies!
How? you ask…
Well, take a right triangle, whose reference angle is 30 degrees. That means the third angle in the triangle must be 60 degrees. Remember it’s a right triangle so one of the angles is 90 degrees already.
Well, by the power of SOH-CAH-TOA, we discover that the sin(30) = ½, and cos(60) = ½. And, 30 + 60 = 90 ! Wow!
Geometric Representation of Cofunctions
Study.com does a great job helping us find trig buddies by examining the word COmplementary.
Sine and COsine are COfunctions. Tangent and COtangent are COfunctions, and Secant and COsecant are COfunctions.
Super!
In this lesson we will look at Reference Angles as they pertain to Cofunctions, in order to help us express a function in terms of the same function of its reference angle.
Additionally, we will find the complement and supplement for given angles. A great way to remember this is by looking at the first letter of each word, as nicely stated by Math is Fun:
C is for Complement which stands for Corner, like a right angle or 90 degrees. S is for Supplement which stands for Straight (remember a straight line is 180 degrees).
Cofunctions – Video
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