Trig Identities
?=sin²(x)-1
-cos²(x)
?=cos²(x)-1
-sin²(x)
Pythagorean Identity in relation to cot & csc
1+cot²(x)=csc²(x) (1+cotangent²(x)=cosecant²(x)
sin(2x)=?
2sinxcosx
tan(2x)=?
2tan(x)/1-tan²(x)
cos x in relation to π/2
cos x=sin(π/2-x)
Reciprocal Identity (cos)
cos(x)=1/sec(x) & sec(x)=1/cos(x) (cosine of x=1/secant of x & vice versa)
cos(x+y)=?
cos(x+y)=cosx*cosy-sinx*siny
cos(x-y)=?
cos(x-y)=cosx*cosy+sinx*siny
?=1-sin²(x)
cos²(x)
cos(2x)=?
cos²(x)-sin²(x) 2cos²(x)-1 1-2sin²(x)
cot x in relation to π/2
cot x=tan(π/2-x)
Ratio Identity (cot)
cot(x)=cos(x)/sin(x) (cotangent of x=cosine of x/sine of x)
csc x in relation to π/2
csc x=sec(π/2-x)
sec x in relation to π/2
sec x=csc(π/2-x)
sin x in relation to π/2
sin x=cos(π/2-x)
Reciprocal Identity (sin)
sin(x)=1/csc(x) & csc(x)= 1/sin(x) (sine of x= 1/cosecant of x & vice versa)
sin(x+y)=?
sin(x+y)=sinx*cosy+cosx*siny
sin(x-y)=?
sin(x-y)=sinx*cosy-cosx*siny
?=1-cos²(x)
sin²(x)
Pythagorean Identity in relation to sin & cos
sin²(x)+cos²(x)=1 (sine²(x)+cosine²(x)=1)
tan x in relation to π/2
tan x=cot(π/2-x)
Reciprocal Identity (tan)
tan(x)=1/cot(x) cot(x)=1/tan(x) (tangent of x=1/cotangent of x & vice versa)
Ratio Identity (tan)
tan(x)=sin(x)/cos(x) (tangent of x=sine of x/cosine of x)
tan(x+y)=?
tan(x+y)=(tanx+tany)/(1-tanx*tany)
tan(x-y)=?
tan(x-y)=(tanx-tany)/(1+tanx*tany)
Pythagorean Identity in relation to tan & sec
tan²(x)+1=sec²(x) (tangent²(x)+1=secant²(x))
cos(x/2)
±√(1+cos(x)/2
tan(x/2)
±√(1-cos(x))/(1+cos(x))
sin(x/2)
±√(1-cos(x)/2