Notation of Inverse Trig Functions
. The domain of
is
, and its range is
.
. Domain:
; range:
.
. Domain:
; range:
.
. Domain:
; range:
.
. Domain:
; range:
.
. Domain:
; range:
.
Example:
, so
. Even though
as well,
is outside of the range for
.
Notes:
, and
.
does NOT equal
. Similarly,
, and NOT
.
Inverse Trig Functions
![{\displaystyle \int \arccos u\mathrm {d} u=u\arccos u-{\sqrt {1-u^{2}}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0afb5eedda89f5e44e04e43076fc8d9f4914ce62)
![{\displaystyle \int \arctan u\mathrm {d} u=u\arctan u-\ln {\sqrt {1+u^{2}}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e9bb94bea296daa0dbaecf09f89dca20c0de1a29)
![{\displaystyle \int \operatorname {arccot} u\mathrm {d} u=u\operatorname {arccot} u+\ln {\sqrt {1+u^{2}}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa465967e2fe2be9af09740ca70406c135cb16ad)
![{\displaystyle \int \operatorname {arcsec} u\mathrm {d} u=u\operatorname {arcsec} u+\ln \left\vert u+{\sqrt {u^{2}-1}}\right\vert +C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/342ed31c18778f68f117bfe8562ecd9ac133f69b)
![{\displaystyle \int \operatorname {arccsc} u\mathrm {d} u=u\operatorname {arccsc} u+\ln \left\vert u+{\sqrt {u^{2}-1}}\right\vert +C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b2027dc1083283e97be811c2da63dc936700c757)
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