Section 5 1 Trigonometric Identities Objectives Identify basic
Section 5. 1 Trigonometric Identities Objectives: - Identify basic trig identities - Use basic trig identities to - find trig values - simplify and rewrite expressions
Identities • An equation is an identity if the left side is equal to the right side for all values of the variable for which both sides are defined.
Trig Identities
Example 1: •
Example 1: •
Pythagorean Identities (sin )2 + (cos )2 = 12 sin 2 + cos 2 = 1
Pythagorean Identities sin 2 + cos 2 = 1 tan 2 + 1 = sec 2 cot 2 + 1 = csc 2
Example 2: •
Cofunction Identities
Odd-Even Identities
Example 3: A) If cos x = – 0. 75, find B) If cos x = 0. 73, find
Simplifying • Helpful Hints – No fractions – 1 trig function – Factor out a GCF – Common Denominators / Conjugate
Example 4: Use identities to simplify •
Example 5: Use identities to simplify A) cos x tan x – sin x cos 2 x B) cos x sin 2 x - cosx
Example 6: Use identities to simplify •
Example 7: Rewrite as an expression that does not involve fractions •
PRACTICE: 1. sin θ sec θ cot θ 2. cot x sec x sin x 3. tan x csc x cos x 4.
Put the steps in order • In a small group, you receive a bag of problems. Each bag contains 3 problems that need to be simplified using identities. Each simplified step is provided, however, you must put the steps in order for each of the 3 problems.
- Slides: 19
