Trigonometric functions encompass a vast array of topics, including sine, cosine, and tangent functions and their graphs. These functions are fundamental to understanding oscillatory behavior and periodic phenomena in mathematics and science.
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
