Daftar identitas-identitas Trigonometri Penting

Identitas trigonometri yang berikut adalah benar untuk semua x dan y, asal kedua ruas terdefinisi pada x dan y yang dipilih.

Identitas ganjil genap

\sin \left( -x \right)=-\sin x

\cos \left( -x \right)=\cos x

\tan (-x)=-\tan x

Identitas ko-fungsi

\sin \left( 90{}^\circ -x \right)=\cos x

\cos \left( 90{}^\circ -x \right)=\sin x

\tan \left( 90{}^\circ -x \right)=\cot x

Identitas phytagoras

{{\sin }^{2}}x+{{\cos }^{2}}x=1

1+{{\tan }^{2}}x={{\sec }^{2}}x

1+{{\cot }^{2}}x={{\csc }^{2}}x

Identitas penambahan

\sin \left( x+y \right)=\sin x\cos y+\cos x\sin y

\cos \left( x+y \right)=\cos x\cos y-\sin x\sin y

\tan \left( x+y \right)=\frac{\tan x+\tan y}{1-\tan x\tan y}

 

Identitas sudut ganda

\sin 2x=2\sin x\cos x

\cos 2x={{\cos }^{2}}x-{{\sin }^{2}}x

=2{{\cos }^{2}}x-1

=1-2{{\sin }^{2}}x

Identitas setengah sudut

\sin \left( \frac{x}{2} \right)=\pm \sqrt{\frac{1-\cos x}{2}}

\cos \left( \frac{x}{2} \right)=\pm \sqrt{\frac{1+\cos x}{2}}

Identitas jumlah

\sin x+\sin y=2\sin \left( \frac{x+y}{2} \right)\cos \left( \frac{x-y}{2} \right)

\cos x+\cos y=2\cos \left( \frac{x+y}{2} \right)\cos \left( \frac{x-y}{2} \right)

Identitas hasil-kali

\sin x\sin y=-\frac{1}{2}\left[ \cos \left( x+y \right)-\cos (x-y) \right]

\cos x\cos y=\frac{1}{2}\left[ \cos \left( x+y \right)+\cos (x-y) \right]

\sin x\cos y=\frac{1}{2}\left[ \sin \left( x+y \right)+\sin (x-y) \right]

Ingat:

\frac{1}{\sin x}=\csc x

\frac{1}{\cos x}=\sec x

\frac{1}{\tan x}=\cot x

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