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Mapping your mind by Kyanna Dyer - Coggle Diagram
Mapping your mind by Kyanna Dyer
The 6 trigonometric functions & their properties
P= (x,y); r= √(x^2+y^2)
sinx= y/r, cosx=x/r, tanx=y/x,cscx=r/y, secx=r/x, cot=x/y
Reciprocal Identities
sinx= 1/cscx, cosx=1/secx, tanx=1/cotx, cscx=1/sinx, secx= 1/cosx, cotx=1/tanx
Quotient Identities
tanx= sinx/cosx, cotx=cosx/sinx
Pythagorean Identities
sin^2x+cos^2x=1
1+tan^2x=sec^2x
1+cot^2x=csc^2x
Even-Odd Identities
sin(-x)=-sinx, csc(-x)=-cscx, cos(-x)=cosx, sec(-x)=secx, tan(-x)=-tanx, cot(-x)=-cotx
Sum and Difference Formulas
sum for tangent= tan(a+B)= tana+ tanB/1-tanatanB
difference for tangent= tan(a-B)= tana- tanB/1+tanatanB
sum for cosine= cos(a+B)=cosacosB-sinasinB,
difference for cosine= cos(a-B)=cosacosB+sinasinB,
sum for sine= sin(a+B)=sinacosB+cosasinB,
difference for sine= sin(a-B)=sinacosB-cosasinB
Double Angle & Half Angle Formula
Double Angle Formulas for tangent and sine--> sin2a=2sinacosa, tan2a=2tana/1-tan^2a,
Double Angle Formulas for cosine --> cos2a=cos^2a-sin^2a, cos2a=2cos^2a-1, cos2a=1-2sin^2a
Half Angle Formulas --> a/2= +- √1-cosa/2, cos 1/2= +-√1+cosa/2, tan a/2= +- √1-cosa/1+cosa, tan a/2= 1-cosa/sina, tan a/2=sina/1+cosa
Use the fundamental identities (6 trig functions, reciprocal identities, quotient identities, Pythagorean identities, and even odd identities) to establish other relationships among trig functions
Difference of two angles- we can place the angle in a standard position and use the distance formula to prve the identity. This formula is then used to prove other identities.
Sum & Difference formulas are used to prove the double angle formulas
Half Angle Formulas are similar to power-reducing formulas. You must find the quadrant to determine if the value is + or -