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