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 Question from Suzanne, a student: I'm a UR University Graduate (with High honours!) but not in math: I'm taking GeoTrig, Sk Learning version, and the text is poorly written. But I was flying through the material until I hit the Trig Identities. I just don't get WHY we have them, why we should know them? What good is this "theory". All that "simplifying" rarely yields a simple-er version! Also, give me advice for how to study them. Thanks Suzanne

Hi Suzanne,

It's not the identities themselves that are important it is the experience you gain by working with them. I know very few identities, mainly

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
sin2(A) + cos2(A) = 1

There are situations in solving practical problems that involve trigonometry where one of these identities or a different trig identity can help simplify the problem or give another way to look at the problem. Knowledge of these few identities and skill with manipulating identities allows me to see other relationships.

Also working with trig identities is one of the few places in the high school curriculum where student are required to construct a mathematical proof. Proofs are at the heart of mathematics and as a mathematician I think it is important that student experience this activity. That being said I don't think trig identities give the optimal experience in proof construction. I don't think this material give much opportunity for ingenuity in the proofs. I would much rather students work with the proofs in Euclidean geometry.