5.1(a) Notes: Using Fundamental Identities Date: 5.1(a) Notes: Using Fundamental Identities   Lesson Objective: Recognize and write the fundamental trig identities. Use the trig iden-tities to simplify trig expressions. CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle. You will need: a separate sheet of paper, graphing calculator

Lesson 1: Fundamental Trig Identities On a separate page, write the following iden-tities.

Lesson 1: Fundamental Trig Identities Reciprocal Identities: sin x = ____ cos x = ____ tan x = ____ csc x = ____ sec x = ____ cot x = ____

Lesson 1: Fundamental Trig Identities Reciprocal Identities: sin x = ____ cos x = ____ tan x = ____ csc x = ____ sec x = ____ cot x = ____ Quotient Identities: tan x = ____ cot x = ____

Lesson 1: Fundamental Trig Identities Pythagorean Identities:

Lesson 1: Fundamental Trig Identities Pythagorean Identities: + = 1 

Lesson 1: Fundamental Trig Identities Pythagorean Identities: + = 1 sin x = + cos x = + tan x = + cot x = +

Lesson 1: Fundamental Trig Identities Use a graphing utility to graph the following: sin x cos x sin π 2 −𝑥 = ?

Lesson 1: Fundamental Trig Identities Cofunction Identities: sin π 2 −𝑥 = cos x cos π 2 −𝑥 = tan π 2 −𝑥 = cot π 2 −𝑥 = csc π 2 −𝑥 = sec π 2 −𝑥 =

Lesson 1: Fundamental Trig Identities Even Identities: cos(-x) = sec(-x) = Odd Identities: sin(-x) = csc(-x) = tan(-x) = cot(-x) =

Lesson 2: Using Identities to Evaluate a Function Use the values sin x = ½ and cos x > 0 to find the values of all six trigonometric functions.

Lesson 3: Simplifying a Trig Expression cos²x csc x – csc x

Lesson 3: Simplifying a Trig Expression csc t – cos t cot t

Lesson 4: Factoring Trigonometric Expressions Factor each expression. 1 – cos²x

Lesson 4: Factoring Trigonometric Expressions Factor each expression. 2 csc²x – 7csc x + 6

Lesson 4: Factoring Trigonometric Expressions Factor each expression. sec²x + 3 tan x + 1

5.1(a): Do I Get It? Yes or No Use the values sec u = - 3 2 and tan u > 0 to find the values of all six trig functions. Simplify sin x cos2x – sin x. Simplify sin t + cot t cos t. Factor sec2 θ – 1. Factor 4 tan2 θ + tan θ – 3. Factor csc2 x – cot x – 3.