Pembezaan fungsi trigonometri

Trigonometri

Sejarah Kegunaan Fungsi Fungsi songsang Bacaan lanjut

Rujukan

Senarai identiti Pemalar tepat Menghasilkan jadual trigonometri

Teori Euclid

Hukum sinus Hukum kosinus Hukum tangen Teorem Pythagoras

Kalkulus

Penggantian trigonometri Kamiran fungsi Pembezaan fungsi Kamiran songsang

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
$\sin(x)$	${d \over dx}\sin(x)=\operatorname {kos} (x)$
$\operatorname {kos} (x)$	${d \over dx}\operatorname {kos} (x)=-\sin(x)$
$\tan(x)$	${d \over dx}\tan(x)={d \over dx}{\biggl (}{\sin(x) \over \operatorname {kos} (x)}{\biggr )}={\operatorname {kos} ^{2}(x)+\sin ^{2}(x) \over \operatorname {kos} ^{2}(x)}=1+\tan ^{2}(x)=\operatorname {sek} ^{2}(x)$
$\operatorname {sek} (x)$	${d \over dx}\operatorname {sek} (x)={d \over dx}{\biggl (}{1 \over \operatorname {kos} (x)}{\biggr )}={\sin(x) \over \operatorname {kos} ^{2}(x)}=\operatorname {sek} (x)\tan(x)$
$\operatorname {kosek} (x)$	${d \over dx}\operatorname {kosek} (x)={d \over dx}{\biggl (}{1 \over \sin(x)}{\biggr )}=-{\operatorname {kos} (x) \over \sin ^{2}(x)}=-\operatorname {kotan} (x)\operatorname {kosek} (x)$
$\operatorname {kotan} (x)$	${d \over dx}\operatorname {kotan} (x)={d \over dx}{\biggl (}{\operatorname {kos} (x) \over \sin(x)}{\biggr )}={-\operatorname {kos} (x)-\sin ^{2} \over \sin ^{2}(x)}=-(1+\operatorname {kot} ^{2}(x))=-\operatorname {kosek} ^{2}(x)$

Fungsi trigonometri songsang

Terbitan pembezaan fungsi trigonometri songsang

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