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Trigonometry Unit 3 - Coggle Diagram
Trigonometry Unit 3
Six Trigonomic Functions
Secant Function : f(x) = sec (x)
Domain: all real numbers
Range: (-infinity, -1] U [1, infinity)
Period: 2pi
Cosecant Function : f(x) = csc (x)
Domain: all real numbers except k pi, pi is an integer
Range: (-infinity, -1] U [1, infinity)
Period: 2 pi
Tangent Function : f(x) = tan (x)
Domain: all real numbers
Range: all real numbers
Period: pi
Cotangent Function : f(x) = cot (x)
Domain: all real numbers except k pi, k is an integer
Range: all real numbers
Period: pi
Cosine Function : f(x) = cos (x)
Domain: all real numbers
Range: [-1, 1]
Period:2pi
Sine Function : f(x) = sin (x)
Domain: all real numbers
Range: [1, 1]
Period: 2pi
Reciprocal, Quotient, Pythagorean, and Even-Odd Identities.
Reciprocal Identities
sin x = 1/csc x
csc x = 1/sin x
cos x = 1/sec x
sec x = 1/cos x
tan x = 1/cot x
cot x = 1/tan x
Quotient Identities
tan x = sin x/cos x
cot x = cos x/sin x
Pythagorean Identities
sin^2x+cos^2x= 1 (used most often)
1+tan^2x= sec^2x
1+cot^2x= csc^2 x
Even-Odd Identities
sin(-x)= - sin x
csc(-x)= - csc x
cos(-x)= cos x
sec(-x)= sec x
tan(-x)= - tan x
cot(-x)= - cot x
Double- Angle and Half- Angle Formulas
Double Angle Formulas
0= theta
sin2 0= 2sin0cos0
tan20= 2tan 0/ 1-tan^20
cos20=cos^0-sin^20
cos= 2cos^20-1
cos20= 1-2sin^20
Half- Angle Formulas
sin a/2= ±√1-cos a / 2
cos a/2= ±√ 1+cos a / 2
tan a/2= ±√1-cos a /1+cos a
tan a/2= 1-cos a / sin a
tan a/2= sin a / 1+cos a
Sum and Difference Formulas
sin (a+b)= sin a cos b+ sin a cos b
sin (a-b)= sin a cos b - cos a sin b
cos (a+b)= cos a cos b - sin a sin b
cos (a-b)= cos a cos b + sin a sin b
tan(a+b)= tana+tan b / 1- tan a tan b
tan (a-b)= tan a- tan b/ 1+ tan a tan b