Download Day III 5.2 day 1

Math Analysis
Day III. Verifying Trigonometric Identities (5.2)
1/17/12
A dog is the greatest gift a parent can give a child. OK, a good education, then a dog. John
Grogan, born March 20, 1957, American journalist and non-fiction writer
You can use trigonometric identities to simplify an expression for a rate of change.
I. Introduction
Match the following words with the example and with the working method.
Expression
3x – 6 = 0
verify
Conditional Equation
3x – 6 = 3(x – 2)
simplify
Identity
3x – 6
solve
What is the difference between an identity and a conditional equation?
Guidelines for Verifying Trigonometric Identities


Work with ______________side of the equation at a time - the more complicated side
first.
______________ for factoring, adding fractions, squaring binomials, or creating
monomial denominators.
Look for fundamental ________________________.

If nothing works, try_________________________ to sines and cosines.

______________________ try something!!!

II. Verifying Trigonometric Identities
Example 1. Verifying a Trigonometric Identity
Verify:
tan2  =
Your Turn:
= csc2 
Example 2. Combining Fractions Before Using Identities
Verify: 2 tan2  =
+
Your Turn:
+
= 2 sec2 
Example 3. Verifying a Trigonometric Identity
Verify: sin2 x(csc x–1)(csc x+1) = 1 - sin2 x
Your Turn: ( 1 – tan )2 = sec2  - 2 tan 
Example 4. Converting to Sines and Cosines
Verify:
+
= sec2   csc 
Your Turn: sec  – tan   sin  = cos 
Example 5. Verifying Trigonometric Identities
Verify:
-
= 5(tan  - sec )
Your Turn:
= 1 + cos 
Example 6. Working with Each Side Separately
Verify:
= sec   csc 
Your Turn: tan   sin  = sec  - cos 
Example 7. Calculus Example
csc4 x cot x = csc2 x(cot x + cot3 x)
Your Turn: cot5  = cot3  csc2  - cot3 