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
Graphs of the trigonometric functions ,the Inverse Sine, Cosine, and Tangent Functions.
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
Tangent Functions
y=tan-1 x and only if x=tan y
Where - infinity< x< infinity and -pi/2
Cosine Function
y=cos-1 x if and only if x= cos y
where -1< x < 1 and 0 < y < pi
Inverse sine function
y=sin-1 x if and only if x=sin y
Where -1
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
Properties of the trigonometric function
Determine the domain and rage
Domain Range
Sin ARN [-1,1), -1< Sin pi<1
Cos ARN [-1,1] -1
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
Cosine Law
a2=b2+c2-2bc cos A
b2=a2+c2-2ac Cos B
c2=a2+b2-2ab Cos C
