University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2020
Views:

104

Pages:

11
Author:

granitt3c2r

Tues, 5/19/20 - Section 7.1 Sunday, May 17, 2020 12:16 PM 7.1 Trig Identities and Simplifying Trig Expressions 1. What is an identity? 2. What are the 3 main types of trig identities? 3. Strategies for simplifying trig expressions. 4. Examples, examples, examples... -57 -√7 Example: 15 + 6x = 1/2 * (32 + 12x) - 1 15 + 6x = 16 + 6x - 1 15]+ 6x = 18 + 6x X=2+1 solution 4=6 Nosolotron (6x)/6 = (6x)/6 x = x < infinite Solutions Identity: An Identity is a type of equation that is true for all values of the variables. 3x = 12 X=4& Not an identity (X + 3 = X + 3)/(iuh*gamma) What are Identities used for?: They are used for simplifying and rearranging algebraic expressions. Example: (a + b) ^ 3 = a ^ 3 + 3a ^ 2 * b + 3a * b ^ 2 + b ^ 3 (x + 4) ^ 3 = x ^ 3 + 3x ^ 2 * 4 + 3x * 16 + 64 x ^ 3 + 12x ^ 2 + 4gamma*x + 64 (a + b)(a - b) = a ^ 2 - b ^ 2 (a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2 What are Trig Identities used for?: We learn to use Trig Identities to help use solve more complicated trig equations when we can't use a graph. There are 3 main types of Trig Identities: 1. Reciprocal Identities 2. Quotient Identities 3. Pythagorean Identities know these already Reciprocal Identities sin theta ne csc(theta) tan theta = 1/(cx + theta) and tan theta = (sin theta)/(cos theta) Quotient Identities 90% X tan theta = y/x cos theta = x sin theta = y Pythagorean Pythagorean Theorem: a ^ 2 + b ^ 2 = c ^ 2 Rewrite using x,y,r. y ^ 2 + x ^ 2 = r ^ 2 Rewrite using trig: **1st identity Divide by sin^2 theta **2nd identity Divide 1 identity by cos^2 theta tan^2 x + 1 = sec^2 (xl) ** 3 ^ (rd) identity sin^2 x = 1 - cos^2 x 3 +4 ne5 3 ^ 2 + 4 ^ 2 = 5 ^ 2 sin theta 1 = csc^2 x - cot^2 x sec^ 2 x-1 ne 1 - sec^2 x * 1 - cos^2 x = sin^2 x 6-4 7 4-6 2 2 cos theta = 1/(se*theta) tan theta = 1/(cot theta) csc theta= 1 s dot in * theta sec(theta) = 1/(omega*os*theta) cot theta = 1/(tan theta) tan^2 x = sec^2 x - 1 sin theta = 1/(csc(theta)) tan theta= 5 dot x*theta cos theta tan^2 x + 1 = sec^2 x cot^2 x = csc^2 x - 1 cot theta= cos theta s dot n*theta cos^2 x = 1 - sin^2 x 1= sec^2 x -tan^ 2 x\ 1 + cot^2 x = csc^2 x (cos^2 theta)/(sin^2 theta) = omega + 9 sin^2 x + cos^2 x = cos^2 x + sin^2 x ((cos theta)/(r * sin theta)) ^ 2 * (c, theta) cos^2 x - 1 = - sin 3 sin^2 x + cos^2 x = 1 c + theta = x/y = sin^2 theta sin^2 x + cos^2 x = 1 1+cot^ 2 x=csc^ 2 x| cos theta 1cos^2 x