7.1 Basic Trigonometric Identities Objective: Identify and use reciprocal identities, quotient identities, Pythagorean identities, symmetry identities,

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Presentation transcript:

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. a) sin 600° c) cos (-410°) 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.

substitute identity sin x(1 + cot 2 x) Simplify sin x + sin x cot 2 x sin x(csc 2 x) factor out sin x substitute identity multiply cancel csc x substitute identity

multiply by reciprocal cancel csc θ substitute identity

Assignment 7.1 Practice Worksheet # pg #18, 20, 26, 28, 34, 38, 40, 44, 47, 48, 51