Such examinations, lead us to three sets of “cofunction” identities:
Notice the connection of the letters C & O:
* sine and cosine cofunctions
* tangent and cotangent cofunctions
* secant and cosecant cofunctions
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.
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