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## TRIGONOMETRY

by: Edmond Thompson Jr.

39

0

4

# TRIGONOMETRY MATH 1303

Edmond Thompson Jr.
UTA
GPA 3.53

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Edmond Thompson Jr. on Thursday October 29, 2015. The Class Notes belongs to MATH 1303 at University of Texas at Arlington taught by Staff in Fall. Since its upload, it has received 39 views. For similar materials see /class/231259/math-1303-university-of-texas-at-arlington in Mathematics (M) at University of Texas at Arlington.

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Date Created: 10/29/15
Trig Cheat Sheet De nition of the Trig Functions Right triangle de nition For this de nition we assume that 0lt9lt or 0 lt9lt90 i h otenuse yp opposite L gt adjacent Sing 2 opp051te 0809 hypotenuse sine X hypotenuse opposne 1 0089 2 adjacent hypotenuse 0089 i hypotenuse adjacent 1 whm 0092 we adjacent opposne x Domain The domain is all the values of 9 that can be plugged into the function 9 Facts and Properties Period Unit circle de nition For this de nition 9 is any angle csc9 1 y sec9 1 x cot9 y The period of a function is the number Tsuchthat f9Tf9 So ifco 11199 3 can Be any angie is a xed number and 9 is any angle we COS can elany ange have the following periods tan9 9 najm n0ili2 271 csce 9mm n0ili2 511W T 1 271 sece 9 nE 71 n0ili2 cosagt9 gt T a cote 93771 n0ili2 tanw9 gt Tzl a Range 271 The range is all possible values to get cscw9 gt T CD out of the function 2n 1ssin9s1 csc921andcsc9 S l Secw9 gt 71 1scos9 s1 secQZIandsecQS l 7T oolttan9ltoo ooltcot9ltoo c tw9 gt Tg 2005 Paul Dawkins Formulas and Identities Tangent and Cotangent Identities sin 9 cos 9 cot 9 cos 9 sm 9 Reciprocal Identities tan9 csc9 sin9 sm 9 csc9 sec9 cos9 cos 9 sec9 cot9 1 tan9 1 tan9 cot9 Pythagorean Identities sin2 9 cos2 9 1 tan2 9 1 sec2 9 1cot2 9 csc2 9 EvenOdd Formulas sin 9 sin9 cos 9 cos 9 tan 9 tan9 csc 9 csc9 sec 9 sec9 cot 9 cot9 Periodic Formulas Ifn is an integer sin 9 27171 sin9 csc9 27m csc9 cos9 27171 cos9 sec9 27171 sec 9 tan9 7171 tan9 cot9 71m cote Double Angle Formulas sin29 2sin9 cos9 cos29 cos2 9 sin2 9 2cos2 9 1 1 2sin2 9 2tan9 tan29 m Degrees to Radians Formulas Ifx is an angle in degrees and t is an angle in radians then 71 t 2 t 180 x Half Angle Formulas 1 sm2 9 51 cos 29 cos2 9 1cos29 1 cos 29 1 cos29 Sum and Difference Formulas sinoc i sinoc cos icosasin tan2 9 cosoc i cosacos isinasin tan a i tan f 1i tanoc tan f Product to Sum Formulas sinasin cosa cosa tanoci cosacos cosa cosa sinacos sina sina cosasin sina sina Sum to Product Formulas sinasin 2sin a L3 L3 cos a 2 sin a 2 2 WW 2 2 cosa cos 2sina jsina 2 2 2 06 sina sin 2cos a cosacos 2cos Cofunction Formulas sin 79cose 4579st 2 2 csc 79 secQ sec 79 cch 2 2 tan 79 cote cot 79 tane 2 2 2005 Paul Dawkins Unit Circle yn01 i 2 2 E 2 2 L 2 k 2 2 E JEJE 2 90 3 x 27 2 7 120 o g 60 4 31 a is 7 23 5 135 45 1 300 150 1 710177 180 0 0 m j 210 0 7 330 1171 5 225 6 3 1 o 43 1 7 5 57v 315 477 240 0 771 4 o 300 1 2 2 L 270 5 4I J 7 3 3 2212 3 2 2 l 2 1 J5 2 2 Y7 For any ordered pair on the unit circle xy 0059 x and 51119 y Example 2005 Paul Dawkins Inverse Trig Functions De nition y sin 1 x is equivalent to x sin y y cos 1 x is equivalent to x cos y y tan 1 x is equivalent to x tany Domain and Range Function Domain Range 71 71 sin391x leSl S S y 2 y 2 ycos 1x leSl OSySn ytan391x ooltxltoo ltylt 2 2 Inverse Properties coscos 1 x sin sin391 x tantan391 x Alternate Notation sin 1 x arcsin x cos 1 x arccos x tan 1 x arctan x Law of Sines Cosines and Tangents cos 1cos9 9 sin391sin9 9 tan 1tan9 9 Law of Sines sinoc sin sinj a b 0 Law of Cosines a2 b2 c2 2bccosoc b2 a2 02 2accos c2 a2 b2 2abcosy Mollweide s Formula ab 005a 39 1 c sm 3 Law of Tangents abtan0 I3 ab tana b c tan y bc tan lt ygt a c tanoc y ac tanay 2005 Paul Dawkins

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