Day 1 ­ Notes ­ Basic Trig Identities
Unit 4
What is an identity? Intro to Trigonometric Identities
EQ: How do I prove trigonometric expressions equivalent?
General Trig Ratio Identities
csc x =
A statement that is valid for all values of the variables in the domain where the expressions are defined.
What are some identities that we are already familiar with from Algebra?
When simplifying a trig expression, try changing everything to terms of sine and cosine.
tan x =
Example 1 : Simplify sec x =
cos x csc x
cot x =
Example 2: Simplify tan x cos x
sin x
Proofs: When in doubt, change everything to sine and cosine. Try to only change one side, not both. Start with the more complicated­looking side.
Example 3: Prove
Example 4: Prove csc x = sec x
cot x
sin x sec x = tan x
1
Day 1 ­ Notes ­ Basic Trig Identities
Example 5: Prove cot x + sec x = cos2x + sin x
sin x cos x
cos2θ + sin2θ = 1
Unit 4
Pythagorean Identities: Derive the Pythagorean Identity from a right triangle
cos2θ + sin2θ = 1
Example 6: tan2x + 1 = sec2x tan2x
csc2x ­ 1
Example 7: Prove sec x = sin x
cot x + tan x
2