# Trig - In a Nutshell Trig In a Nutshell Help Im trapped in a nutshell The Unit Circle (0,1) +,+ -,+ (1,0) (-1,0) +,-

-,(0,-1) Te rm in al ra y 2 +

- 3 2 2 These are the reference triangles 1 30 1 1 2

6 45 2 2 4 2 2 3 2 3 2 1

60 3 1 2 Trigonometric Functions r y sin opp y hyp r

adj x cos hyp r sin opp y tan cos adj x x csc 1 hyp r

sin opp y sec 1 hyp r cos adj x cot 1 cos adj x tan sin opp y

The Identities 2 2 sin x cos x 1 2 2 2 2 1 tan x sec x 1 cot x csc x

Lets go graphing p.s. are cos x and sin x odd or even functions? y afun( bx c) d d? Move graph c? Moves graph a? Changes Amplitude b? Changes Period 2 coeffof x Graphing Trig Functions

(my method) Sin/Cos 1. Determine New Start: Set Argument = 0 2. Determine New End: Set Argument = 2 (or New Start + Period) 3. Find 3 midpoints 4. Plot these 5 points Graphing Trig Functions (my method) Tan/Cot/Sec/Csc 1. Determine 3 New Asymptotes

Set Argument = Old Asymptotes and solve for x 2. Find 2 midpoints 3. Plot these 2 points 4. Sketch the functions according to what they looked like before. Angle Addition Formulas cos A B cosAcosB sin AsinB cos A B cosAcosB sin AsinB sin A B sin AcosB cosAsinB sin A B sin AcosB cosAsinB tan A tanB tan A B 1 tan A tanB tan A tanB tan A B 1 tan A tanB

Double/Half Angle cos2A cos2 A sin2 A sin2A 2sin AcosA 2tan A tan2A 1 tan2 A Double/Half Angle A 1 cosA sin 2 2 A

1 cosA cos 2 2 A sin A 1 cosA tan 2 1 cosA sin A c2 a2 b2 2abcosC Law of Cosines

Inverse Trig For sin-1x, csc-1x, tan-1x QI or QIV (go clockwise!) y 2 2 For cos-1x, sec-1x, cot-1x QI or QII 0 y