Students should already know the even-odd identities for \(\sin\) and \(\cos.\) Start this lesson by asking students to determine which of the six basic trig functions are even, which are odd, and which are neither, given a graph of each function. After that, ask students how we could prove each case algebraically, using only our knowledge of the reciprocal identities, and the fact that \(\sin\) is odd, and \(\cos\) is even? Next, students will use the even-odd identities to evaluate trig functions and simplify trig expressions.
Conclude by giving your students these challenges:
Mentally determine the angle:
Here's the solution.