Trigonometry formulas

trig properties and trig identities

reciprocal identity of sin

sinΘ=1/cscΘ

reciprocal identity of cos

cosΘ=1/secΘ

reciprocal identity of tan

tanΘ=1/cotΘ

reciprocal identity of csc

cscΘ=1/sinΘ

reciprocal identity of sec

secΘ=1/cosΘ

reciprocal identity of cot

cotΘ=1/tanΘ

pythagorean theorem

a²+b²=c²

even property of cos

cos(-Θ)=cosΘ

even property of sec

sec(-Θ)=Θ

odd property of sin

sin(-Θ)=-sinΘ

odd property of tan

tan(-Θ)=-tanΘ

odd property of csc

csc(-Θ)=-cscΘ

odd property of cot

cot(-Θ)=-cotΘ

periodic property of sin

sin(Θ +- 2πn)=sin Θ

periodic property of cos

cos(Θ +- 2πn)=cos Θ

periodic property of tan

tan(Θ +- πn)=tan Θ

quotient identity of tan

tanΘ=sinΘ/cosΘ

quotient identity of cot

cotΘ=cosΘ/sinΘ

pythagorean identity equal to 1

sin²Θ+cos²Θ=1

pythagorean identity of csc²Θ

1+cot²Θ=csc²Θ

pythagorean identity of sec²Θ

tan²Θ+1=sec²Θ

cofunction property of sinΘ

sinΘ=cos(90°-Θ)

cofunction property of tanΘ

tanΘ=cot(90°-Θ)

cofunction property of sec

secΘ=csc(90°-Θ)

cofunction property of cos

cosΘ=sin(90°-Θ)

cofunction property of cot

cotΘ=tan(90°-Θ)

cofunction property of csc

cscΘ=sec(90°-Θ)

area of a circle

A=πr²

circumference of a circle

C=2πr

area of a triangle

A=1/2bh

area of a sector (degrees and radians)

A=1/2r²Θ_rad

central angle, arc, and radius

^radΘ=s^{arc length}/r^radius

degrees to radians

r=π/180

radians to degrees

d=180/π

angular speed

w=2π ⨉ # of turns/time

linear speed

V=r ⨉ w