Such examinations, lead us to three sets of “cofunction” identities:


Also written:


Notice the connection of the letters C & O:
* sine and cosine cofunctions
* tangent and cotangent cofunctions
* secant and cosecant cofunctions
* complementary


1. Find a Value of θ  for which sin θ = cos 15º is true
Solution: Since sine and cosine are cofunctions, we know that the value will be the complement of 15º.
Answer: 75º

2. Write the expression tan 265º as the function of an acute angle of measure less than 45º. Solution: The 265º angle is in the third quadrant with a reference angle of 85º. So we could write:
tan 265º = tan 85º. But the question wants an angle less than 45º, so we use our cofunctions.
tan 85º = cot 5º.
Answer: cot 5º