Reciprocal Identities [ edit ]
sin
u
=
(
1
csc
u
)
{\displaystyle \sin u=\left({\frac {1}{\csc u}}\right)}
cos
u
=
(
1
sec
u
)
{\displaystyle \cos u=\left({\frac {1}{\sec u}}\right)}
tan
u
=
(
1
c
o
t
u
)
{\displaystyle \tan u=\left({\frac {1}{\ cotu}}\right)}
csc
u
=
(
1
sin
u
)
{\displaystyle \csc u=\left({\frac {1}{\sin u}}\right)}
sec
u
=
(
1
cos
u
)
{\displaystyle \sec u=\left({\frac {1}{\cos u}}\right)}
cot
u
=
(
1
tan
u
)
{\displaystyle \cot u=\left({\frac {1}{\tan u}}\right)}
Pythagorean Identities [ edit ]
sin
2
u
+
cos
2
u
=
1
{\displaystyle \sin ^{2}u+\cos ^{2}u=1}
1
+
tan
2
u
=
sec
2
{\displaystyle 1+\tan ^{2}u=\sec ^{2}}
1
+
cot
2
u
=
csc
2
u
{\displaystyle 1+\cot ^{2}u=\csc ^{2}u}
Quotient Identities [ edit ]
tan
u
=
(
sin
u
cos
u
)
{\displaystyle \tan u=\left({\frac {\sin u}{\cos u}}\right)}
cot
u
=
(
cos
u
sin
u
)
{\displaystyle \cot u=\left({\frac {\cos u}{\sin u}}\right)}
Co-Function Identities [ edit ]
sin
(
(
π
2
)
−
u
)
=
cos
u
{\displaystyle \sin(\left({\frac {\pi }{2}}\right)-u)=\cos u}
cos
(
(
π
2
)
−
u
)
=
sin
u
{\displaystyle \cos(\left({\frac {\pi }{2}}\right)-u)=\sin u}
tan
(
(
π
2
)
−
u
)
=
cot
u
{\displaystyle \tan(\left({\frac {\pi }{2}}\right)-u)=\cot u}
csc
(
(
π
2
)
−
u
)
=
sec
u
{\displaystyle \csc(\left({\frac {\pi }{2}}\right)-u)=\sec u}
sec
(
(
π
2
)
−
u
)
=
csc
u
{\displaystyle \sec(\left({\frac {\pi }{2}}\right)-u)=\csc u}
cot
(
(
π
2
)
−
u
)
=
tan
u
{\displaystyle \cot(\left({\frac {\pi }{2}}\right)-u)=\tan u}
Even-Odd Identities [ edit ]
sin
(
−
u
)
=
−
sin
(
u
)
{\displaystyle \sin(-u)=-\sin(u)}
cos
(
−
u
)
=
c
o
s
(
u
)
{\displaystyle \cos(-u)=cos(u)}
tan
(
−
u
)
=
−
tan
(
u
)
{\displaystyle \tan(-u)=-\tan(u)}
csc
(
−
u
)
=
−
csc
(
u
)
{\displaystyle \csc(-u)=-\csc(u)}
sec
(
−
u
)
=
sec
(
u
)
{\displaystyle \sec(-u)=\sec(u)}
cot
(
−
u
)
=
−
cot
(
u
)
{\displaystyle \cot(-u)=-\cot(u)}
This material was adapted from the original CK-12 book that can be found here . This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License
