Precalc wup 216 Using trig identities 2 Simplify

7. 2 Verifying Trig Identities Verifying trig identities algebraically involves transforming one side of

Suggestions for verifying : w Start with the more complicated side: you are trying

Review of Pythagorean identities Can also be written: cos 2 q = 1 –

Ex 1: Verify the identity sec 2 x – tanxcotx = tan 2 x

Ex 2: You try: Hint: you should recognize this is an identity Substituted a

Ex 3: find a numerical value of one trig function of x if You

Ex 4: little more difficult, but you can do it: find a numerical value

Summary: w Homework: w Tues/Wed pg 434 # 13 -28 w Thur pg 434

Slides: 9

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Pre-calc w-up 2/16 Using trig identities 2. Simplify cos 2 x tan 2 x + cos 2 x Answers: 1. + 5/13 2. -cos 50 o 3. 1

7. 2 Verifying Trig Identities Verifying trig identities algebraically involves transforming one side of the equation into the same form as the other side using basic trig identities and properties of algebra.

Suggestions for verifying : w Start with the more complicated side: you are trying to get it to match the simpler side. w Get a common denominator w Substitute one or more basic trig functions. – Ex: you see 1, replace it with sin 2 x + cos 2 x w Factor or multiply to simplify expressions – Ex: sin 2 x – cos 2 x = (sinx – cosx)(sinx + cosx) w Multiply expression by an expression of 1 – Remember the fancy form of 1, same #/same# w Express all trig function in terms of sine and cosine – Ex: you see secx replace it with 1/cosx

Review of Pythagorean identities Can also be written: cos 2 q = 1 – sin 2 q (subtracted sin 2 from both sides) or : sin 2 q = 1 – cos 2 q What about these: : sin 2 q – 1 = – cos 2 q – 1 = – sin 2 q tan 2 q = sec 2 q – 1 sec 2 q – tan 2 q = 1 cot 2 q = csc 2 q – 1 csc 2 q – cot 2 q = 1

Ex 1: Verify the identity sec 2 x – tanxcotx = tan 2 x Which side should we start with? left w Re-write everything using sin & cosine w Simplify 2 x with w Substitute sec 2 x – 1 = a basic trig function tan 2 x + 1 – 1 = w Simplify tan 2 x = tan 2 x w Yeah the right side matches the left

Ex 2: You try: Hint: you should recognize this is an identity Substituted a basic a trig identity Simplified Wrote it as sine and cosine simplified

Ex 3: find a numerical value of one trig function of x if You can work with both sides of the equation in these type of problems w Start by rewriting using sine/cosine w Simplify w Keep simplifying w Goal – to write it as ONE trig function

Ex 4: little more difficult, but you can do it: find a numerical value of one trig function of x if w How to start oh how to start? I know lets get a common denominator

Summary: w Homework: w Tues/Wed pg 434 # 13 -28 w Thur pg 434 # 29 -35 and 7. 1 -7. 2 ws w You must show your work