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3.9 Proving Trig Identities

In this lesson, we explore how to prove trigonometric identities using fundamental identities. The best approach is to start with one side of the equation and manipulate it algebraically or use fundamental identities to show it is equivalent to the other side. There are no strict rules, so experimentation is encouraged. Utilize hints like writing in component parts, combining fractions over a common denominator, multiplying by the conjugate, and applying Pythagorean identities. Dive into practice problems to reinforce your understanding of proving these identities.

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3.9 Proving Trig Identities

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  1. 3.9 Proving Trig Identities

  2. Using fundamental identities (from 3-8), we can prove other identities Best way is to start with one side and manipulate algebraically or use fundamental identities to get it to be equivalent to other side Note: There are no “hard fast” rules to adhere to… sometimes we just have to try something. Hints: – try writing in its component parts or reciprocal – add fractions (common denominator) – multiply fraction by conjugate of bottom – utilize Pythagorean identities If it asks for a “counterexample” you need to find justone value that it will notworkfor. (it might actually work for some values – so think about your choice) (all sines & cosines)

  3. Let’s try some!!! There are 6 problems around the classroom. Work your way around the room doing as many problems as you can Use your friends for help

  4. Homework #309 Pg 174 #1–49 odd

  5. Ex 1) Prove: Work more complicated side

  6. Ex 2) Prove: Work this side Write in terms of sinϕ & cosϕ • PythagIdent • (cos2θ + sin2θ = 1)

  7. Work this side Ex 3) Prove: Mult by conj of bottom • Pythag identity (cos2θ + sin2θ = 1) 1 secθ & cosθ are reciprocals!

  8. Work this side Ex 4) Prove: Write tanθ in terms of sinθ & cosθ cscθ & sinθ are reciprocals! • Use Pythag identity (cos2θ + sin2θ = 1) cosθ & secθ are reciprocals!

  9. Ex 5) Show that sin(β + θ) = sinβ + sinθ is not an identity. You just need 1 counterexample. There are lots of answers!! Here is just one: LHS: RHS:

  10. Ex 6) Prove: Work this side Diff of 2 squares 1 Pythag identity (cos2θ + sin2θ = 1)

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