7 1 Basic Trigonometric Identities Objective Identify and
7. 1 Basic Trigonometric Identities Objective: Identify and use reciprocal identities, quotient identities, Pythagorean identities, symmetry identities, and opposite angle identities.
Prerequisites (assumed skills) • • Foiling Factoring Solving proportions Reducing Fractions Adding Fractions Subtracting Fractions Multiplying Fractions Dividing Fractions
Whenever you are “stuck”… •
Prove that sin x cos x = tan x is NOT a trigonometric identity by producing a counterexample. ?
Use the given information to find the trigonometric value. Choose an identity that involves cos θ and sec θ.
Use the given information to find the trigonometric value. 1+ cot 2 θ = csc 2 θ
Express each value as a trigonometric function of an angle in Quadrant I. Subtract or add 360° or 2π until you get back to 0° to 360° or 0π to 2π. Find the reference angle. Use All Sisters Trade Clothes to get proper sign based on quadrant. a) sin 600° c) cos (-410°)
Simplify sin x + sin x cot 2 x sin x(1 + cot 2 x) sin x(csc 2 x) factor out sin x substitute identity multiply cancel substitute identity csc x
substitute identity multiply by reciprocal cancel substitute identity csc θ
Assignment 7. 1 Practice Worksheet #1 -10 7. 1 pg 427 -428 #18, 20, 26, 28, 34, 38, 40, 44, 47, 48, 51
- Slides: 10
