Trigonometric

Cosine Law

a2=b2+c2-2bc cos A
b2=a2+c2-2ac Cos B
c2=a2+b2-2ab Cos C

Angles and Trigonometric formulas

The Unit Circle

sin=opposite side /hypotenuse
cos =adjacent side /hypotenuse
tan =opposite side/adjacent side
csc =hypotenuse/opposite side
sec =hypotenuse/adjacent side
cot=adjacent side/opposite side

sin(900 -<a ) = cos A
Cos(900-<A)=Sin A
tan(900-<A)=cot A
Cot(900-<a)=tan A
sec(900-<a)=cosec A
Coses(900-<a)=sec A

Properties of the trigonometric function^

Determine the domain and rage

sin=y
scs=1/y
cos = x
sec=1/x
tan=y/x
cot=x/y

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Domain Range
Sin ARN [-1,1), -1< Sin pi<1
Cos ARN [-1,1] -1<cos pi<1
Tan pi# pi/2 ,3pi/2 (infinity , -infinity), tan pi < infinity
5pi/2,....
CSC pi#0,pi,2pi,.... (-infinity , -1]u[1,infinity)
Sec pi#pi/2,3pi/2,5pi/2,... (-infinity,-1]u[1,infinity)
Cot pi#o,pi,2pi,... (-infinity, infinity), -infinity< cot pi<infinity

Sine Law

Sin A/a=Sin B/b=Sin C/c
SinA/a=SinB/b ; SinA/a=SinC/c ; SinB/b=Sinc/c
A+B+C=180o

Graphs of the trigonometric functions ,the Inverse Sine, Cosine, and Tangent Functions.

Inverse sine function
y=sin-1 x if and only if x=sin y
Where -1<x<=1 and -pi/2<y<pi/2


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Cosine Function
y=cos-1 x if and only if x= cos y
where -1< x < 1 and 0 < y < pi

Tangent Functions
y=tan-1 x and only if x=tan y
Where - infinity< x< infinity and -pi/2<y<pi/2

Graphs of sine and cosine funtion :
y=f(x)=sin x
y=f(x)=cos x
y=f(x)=tan x
y=f(x)=csc x
y=f(x)=secx
y=f(x)=cotx

Trigonometric Equations and Trigonometric Identities

- Quotient Identities
tan pi= sin pi/cos pi
cot pi= cos pi/sin pi
- Reciprocal Identities
csc pi=1/sin pi
sec pi=1/cos pi
cot pi=1/tan pi
- Pythagorean Identities
sin2pi+cos2pi=1
tan2pi+1=sec2pi
cot2pi+1=csc2pi
-Even-Odd Identities
sin(-pi)= - sin pi
cos(-pi)=cos pi
tan(-pi)=-tan pi
csc(-pi)= -csc pi
sec(-pi)=sec pi
cot(-pi)=-cot pi