Formulas

These formulas will help you in this wonderful world of math!

Trigonometric Formulas and Identities

A. Basic and Reciprocal Functions
SinA=Opp/Hyp. CscA=Hyp/Opp
CosA=Adj/Hyp. SecA=Hyp/Adj
TanA=Opp/Adj. CotA=Opp/Adj

B. Reciprocal Relation
SinX=1/CscX. CscX=1/SinX
CosX=1/SecX. SecX=1/CosX
TanX=1/CotX. TanX=1/TanX

C. Pythagorean Theorem
Sin²X+cos²X=1
Tan²X+1=sec²X
cot²X+1=csc²X

E. By Definition
TanX=SinX/CosX. CotX=CosX/SinX

F. Functions of Twice an Angle
Sin2X=2sinXcosX
Cos2X=Sin²X-cos²X=2cos²X-1=1-2sin²X
Tan2X=2TanX/1-tanX
Cot2X=cot²X-1/2cotX

CALCULUS

A.  Derivatives

1. Trigonometric

SinU=cosUdU
CosU=-sinUdU
TanU=sec²UdU
CscU=-cotUcscUdU
SecU=tanUsecUdU
CotU=-csc²UdU

2. Logarithmic

lnu= [1/u]•du

logu=[loge/u]•du

3. Exponential

a^u=a^ulna•du

e^u=e^u•du

u^v=u^v[(v/u)•du+lnu•dv]•du

B. Integral

∫sinxdx=-cosx+c.  ∫secxtanxdx=-secx +c

∫cosxdx=sinx+c. ∫cscxcotxdx=-cscx+c

∫sec²xdx=tanx+c.  ∫csc²xdx=-cotx+c