Trigonometric Identities
cos^2(x)=
(1+cos(2x))/2
tan^2(x)=
(1-cos(2x))/(1+cos(2x))
sin^2(x)=
(1-cos(2x))/2
tan(x/2)= (sine in denominator)
(1-cos(x))/sin(x)
cos(a)cos(b)=
(cos(a-b)+cos(a+b))/2
sin(a)sin(b)=
(cos(a-b)-cos(a+b))/2
sin(a)cos(b)=
(sin(a+b)+sin(a-b))/2
cos(a)sin(b)=
(sin(a+b)-sin(a-b))/2
tan(a+b)=
(tan(a)+tan(b))/(1-tan(a)tan(b))
tan(a-b)=
(tan(a)-tan(b))/(1+tan(a)tan(b))
cos(a)-cos(b)=
-2sin((a+b)/2)sin((a-b)/2)
cot(-x)=
-cot(x)
csc(-x)=
-csc(x)
sec(-x)=
-sec(x)
sin(-x)=
-sin(x)
tan(-x)=
-tan(x)
cos(2x)= (in terms of sine)
1-2sin^2(x)
cos(a)+cos(b)=
2cos((a+b)/2)cos((a-b)/2)
sin(a)-sin(b)=
2cos((a+b)/2)sin((a-b)/2)
cos(2x)= (in terms of cosine)
2cos^2(x)-1
Period of cosecant (in terms of pi)
2pi
Period of cosine (in terms of pi)
2pi
Period of secant (in terms of pi)
2pi
Period of sine (in terms of pi)
2pi
sin(a)+sin(b)=
2sin((a+b)/2)cos((a-b)/2)
sin(2x)=
2sin(x)cos(x)
tan(2x)=
2tan(x)/(1-tan^2(x))
cos(a-b)=
cos(a)cos(b)+sin(a)sin(b)
cos(a+b)=
cos(a)cos(b)-sin(a)sin(b)
Cofunction of sin(x) (in terms of pi)
cos(pi/2-x)
1/sec(x)=
cos(x)
cos(2x)= (in terms of sine and cosine)
cos^2(x)-sin^2(x)
Cofunction of tan(x) (in terms of pi)
cot(pi/2-x)
1/tan(x)=
cot(x)
cos(x)/sin(x)=
cot(x)
Pythagorean identity for cotangent and cosecant:
cot^2(x)+1=csc^2(x)
Cofunction of sec(x) (in terms of pi)
csc(pi/2-x)
1/sin(x)=
csc(x)
Period of cotangent (in terms of pi)
pi
Period of tangent (in terms of pi)
pi
Cofunction of csc(x) (in terms of pi)
sec(pi/2-x)
1/cos(x)=
sec(x)
sin(a+b)=
sin(a)cos(b)+cos(a)sin(b)
sin(a-b)=
sin(a)cos(b)-cos(a)sin(b)
Cofunction of cos(x) (in terms of pi)
sin(pi/2-x)
1/csc(x)=
sin(x)
tan(x/2)= (sine in numerator)
sin(x)/(1+cos(x))
Pythagorean identity for sine and cosine:
sin^2(x)+cos^2(x)=1
Cofunction of cot(x) (in terms of pi)
tan(pi/2-x)
1/cot(x)=
tan(x)
sin(x)/cos(x)=
tan(x)
Pythagorean identity for tangent and secant:
tan^2(x)+1=sec^2(x)
cos(x/2)=
±√((1+cos(x))/2)
tan(x/2)= (with √)
±√((1-cos(x))/(1+cos(x)))
sin(x/2)=
±√((1-cos(x))/2)
cos(-x)=
cos(x)
