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# Pembezaan fungsi trigonometri

 Trigonometri Rujukan Teori Euclid Kalkulus

Pembezaan fungsi trigonometri merangkumi proses-proses matematik pembezaan kepada suatu fungsi trigonometri, yakni kadar perubahan berdasarkan suatu pemalar.

Semua hasil pembezaan bagi fungsi trigonometri boleh diterbitkan melalui proses pembezaan sin(x) dan kos(x). Peraturan hasil bahagi kemudiannya digunakan untuk menerbitkan hasil-hasil pembezaan lain.

## Terbitan fungsi-fungsi trigonometri

### Fungsi trigonometri asas

Terbitan pembezaan fungsi trigonometri asas
Fungsi Terbitan pembezaan
${\displaystyle \sin(x)}$ ${\displaystyle {d \over dx}\sin(x)=\operatorname {kos} (x)}$
${\displaystyle \operatorname {kos} (x)}$ ${\displaystyle {d \over dx}\operatorname {kos} (x)=-\sin(x)}$
${\displaystyle \tan(x)}$ ${\displaystyle {d \over dx}\tan(x)={d \over dx}{\biggl (}{\sin(x) \over \operatorname {kos} (x)}{\biggr )}={\operatorname {kos} ^{2}(x)+\sin ^{2}(x) \over \operatorname {kos} ^{2}(x)}=1+\tan ^{2}(x)=\operatorname {sek} ^{2}(x)}$
${\displaystyle \operatorname {sek} (x)}$ ${\displaystyle {d \over dx}\operatorname {sek} (x)={d \over dx}{\biggl (}{1 \over \operatorname {kos} (x)}{\biggr )}={\sin(x) \over \operatorname {kos} ^{2}(x)}=\operatorname {sek} (x)\tan(x)}$
${\displaystyle \operatorname {kosek} (x)}$ ${\displaystyle {d \over dx}\operatorname {kosek} (x)={d \over dx}{\biggl (}{1 \over \sin(x)}{\biggr )}=-{\operatorname {kos} (x) \over \sin ^{2}(x)}=-\operatorname {kotan} (x)\operatorname {kosek} (x)}$
${\displaystyle \operatorname {kotan} (x)}$ ${\displaystyle {d \over dx}\operatorname {kotan} (x)={d \over dx}{\biggl (}{\operatorname {kos} (x) \over \sin(x)}{\biggr )}={-\operatorname {kos} (x)-\sin ^{2} \over \sin ^{2}(x)}=-(1+\operatorname {kot} ^{2}(x))=-\operatorname {kosek} ^{2}(x)}$

### Fungsi trigonometri songsang

Terbitan pembezaan fungsi trigonometri songsang
Fungsi Terbitan
${\displaystyle \arcsin(x)}$ ${\displaystyle 1 \over {\sqrt {1-x^{2}}}}$
${\displaystyle \operatorname {arccos} (xc)}$ ${\displaystyle -1 \over {\sqrt {1-x^{2}}}}$
${\displaystyle \arctan(x)}$ ${\displaystyle 1 \over 1+x^{2}}$
${\displaystyle \operatorname {arcsec}(x)}$ ${\displaystyle 1 \over |x|{\sqrt {1-x^{2}}}}$
${\displaystyle \operatorname {arccsc}(x)}$ ${\displaystyle -1 \over |x|{\sqrt {1-x^{2}}}}$
${\displaystyle \operatorname {arccot}(x)}$ ${\displaystyle -1 \over 1+x^{2}}$