Students will learn what the Pythagorean identities are, why they're true.
Prove the Pythagorean identities by blackpenredpen
Next, students will learn how to find the value of \(\cos \theta,\) or \(\tan \theta,\) given \(\sin \theta\) and the quadrant of \(\theta.\) They'll also learn how to find \(\sin \theta,\) or \(\tan \theta,\) given \(\cos \theta\) and the quadrant of \(\theta.\)
Using the Pythagorean trig identity by Khan Academy
Use the Pythagorean identity by Khan Academy
After that, students will learn how to use the Pythagorean identities to prove certain trig identities. See the first two problems in this video. Next, students will simplify several rational trig expressions. To simplify these expressions, students will use the Pythagorean identities, as well as basic trig identities, such as the reciprocal identities.
Conclude by giving your students these challenges: