Trigonometrijske funckije
Trigonometrijski identiteti
Veze trigonometrijskih funkcija
\( \sin ^{2} x+\cos ^{2} x=1 \)
\( \cos \left(\frac{\pi}{2}-x\right)=\sin x \quad \sin \left(\frac{\pi}{2}-x\right)=\cos x \)
\( \operatorname{tg} x=\frac{1}{\operatorname{ctg} x} \)
\( \sin x=\pm \frac{\operatorname{tg} x}{\sqrt{1+\operatorname{tg}^{2} x}} \quad \operatorname{tg} x=\pm \frac{\sin x}{\sqrt{1-\sin ^{2} x}} \)
\( \cos ^{2} x=\frac{1}{1+\operatorname{tg}^{2} x} \quad \operatorname{tg}x = \pm \frac{\sqrt{1-\cos ^{2} x}}{\cos x} \)
Adicijske formule
\( \sin (x \pm y)=\sin x \sin y \pm \cos x \cos y \)
\( \cos (x \pm y)=\cos x \cos y \mp \sin x \sin y \)
\( \operatorname{tg}(x \pm y)=\frac{\operatorname{tg} x \pm \operatorname{tg} y}{1 \mp \operatorname{tg} x \operatorname{tg} y} \)
\( \operatorname{ctg}(x \pm y)=\frac{\operatorname{ctg} x \operatorname{ctg} y \mp 1}{\operatorname{ctg} x \pm \operatorname{ctg} y} \)
Formule dvostrukog kuta
\( \sin 2 x=2 \sin x \cos x \)
\( \cos 2 x=\cos ^{2} x-\sin ^{2} x \)
\( \operatorname{tg} 2 x=\frac{2 \operatorname{tg} x}{1-\operatorname{tg}^{2} x} \)
Formule polovičnog kuta
\( \sin \frac{\alpha}{2}=\sqrt{\frac{1-\cos \alpha}{2}} \)
\( \cos \frac{\alpha}{2}=\sqrt{\frac{1+\cos \alpha}{2}} \)
Zadatci s državne mature:
Trigonometrijski identiteti
