Trigonometric Identities Notes and Homework Solution

University:
Cornell University
Course:
MATH 1110 | Calculus I
Academic year:

2023
Views:

443

Pages:

10
Author:

Jamarcus Cruz

Advanced Math tan0 = Trigonometric Identities [Day 1) �0- C,()c; csc0 = \ I sec0 '\ I i = Lf)S(r- 40'1&Pythagorean Identity CJ9-0..e�0 cot0 = cofe- e- NOTES [('\ l'\C l. -UJ� e I � � 1..e-,::. j \"\ I Solve the Pythagorean Identity for cos 20 [,__to---�'J.---\---. 4,wl-1 e- :::. (�1.e ,, = ---, 0-J _ in;,,.20 ti_,, ty...,fo..,.r....s,_, Solve the Pythagorean lde;.;.n_, .;..___ --:=-----, 1-r.,os "ltr] Take the Pythagorean Identity and divide every single term by cos 20 [I + :ta-ni.� :: _, Solve the above equation for tan20 2- AU. �1 l�1.& -:: Al�}-(9 -, -I -/ Take the Pythagorean Identity and divide every single term by sin20 l CPl-1-t, +- I _, -== tsc}·�/ Solve the above equation for cot20 Some other identities: sin0 = \ ,. -CSL(9- -, cos0 = tan0 = Sill . 0 1 1 = cos 0 cos0 cot 0 = - cot0 = tan 0 = --:----sm 0 sin 0 tan 0 = s0 tan0 = cot fJ cos 2 0 + sin 2 0 = 1 sin 2 0 = 1 - cos 2 0 cos 2 0 = 1 - sin 2 0 1 + tan 2 0 = sec 2 0 tan 2 0 = sec 2 0 - 1 - tan 2 0 = 1 - sec 2 0 1 + cot 2 0 = csc 2 0 cot 2 0 = csc 2 0 - 1 - cot2 0 = 1 - csc 2 0 co cos0 1 1 sec0 csc0 0 ' 1 = sec0 = csc sin0 1 -�-.-'0---1 Use Trigonometric Identities to write each expression in terms of a single trigonometric identity \r,t� or a constant. � • � � =a osB b. Example 1: .i\W'\'L6- - 4kn<9- � �- � � ill Simplify the complex fraction. Example 2: 2 a. 3 4 15 2 5 c. 3 5 ' '=- �".:2----.:,, ,_c;::rc;- � s: l!.,L-- - -Z.., ....,.,. ']_ 4 5 b. T 35 1 d. l 2

Trigonometric Identities Notes and Homework Solution

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