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## Trigonometry

by: Joseph Notetaker

8

0

3

# Trigonometry MTH 181

Joseph Notetaker
MSU

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These are the notes for 3.1 and 3.2
COURSE
Trigonometry
PROF.
Micheal E. Cagle
TYPE
Class Notes
PAGES
3
WORDS
CONCEPTS
Math
KARMA
25 ?

## Popular in Math

This 3 page Class Notes was uploaded by Joseph Notetaker on Friday April 15, 2016. The Class Notes belongs to MTH 181 at Missouri State University taught by Micheal E. Cagle in Spring 2016. Since its upload, it has received 8 views. For similar materials see Trigonometry in Math at Missouri State University.

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Date Created: 04/15/16
Homework 3.1 and 3.2 Non right triangles require a different method The law of sines: sinα sinβ sinγ = = a b c Five types of problems ASA AAS ASS SAS SSS AAS (angle angle side) o o o α = 37 β = 87 a = 17 All angles still add up to 180 o α = 37 a =17 17sin87 β = 87 o b = sin37 = 28.2 17sin56 o γ = 56 c = sin37 =23.4 If sin > 1 there is no triangle In an ASS (angle side side) problem there can be two triangles (if the angle measurement of triangle 2 is > 180 there is only one triangle) o γ = 33 c = 37 a = 44 This problem has 2 triangles sin33∗44 o o o α = 37 = 40.4 a = 44 α2= (180 – 40.4 ) o =139.6 a2= 44 β = 106.6 o b = 65.1 β2= (180 – 106.6 ) = 7.4 o b2= 8.7 γ = 33 o c = 37 γ 2 33 o c2= 37 The Longest side will correspond to the widest angle and vice versa (there is no ratio) For a SAS (side angle side) or an SSS (side side side) problem you need the law of cosines The law of cosines: 2 2 2 C =A +B -2ABcosγ o α = 117 b = 19 c = 25 (This problem needs the law of cosines because the angle is not opposite to a side) 2 2 2 o A = (19) + (25) – 2(19)(25)cos117 = A = 37.6 o α = 117 a = 37.6 sin117∗19 o β = 37.6 = 26.8 b = 19 o γ = 36.2 c = 25 Here’s another one: A = 23 B = 42 C = 59 (Since this problem has all sides and no angles we have to approach it differently) 2 2 2 (59) = (23) + (42) – 2(23)(42)cosγ 1188 = -1932cosγ o cosγ = -0.614906832 = γ = 127.9 sin127.9∗23 α = 59 = 17.9 o a = 23 β = 34.8o b = 42 γ = 127.9 o c = 59 Lastly we have some formulas for area: For the law of sines: 1 absinγ A = 2 For the law of cosines: A = √S(S−a)(S−b)(S−c) 1 S = 2(a+b+c)

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