Las relaciones directas entre las razones trigonométricas son: [br][br][math]sen^2\alpha+cos^2\alpha=1[/math][br][br][math]tg\alpha=\frac{sen\alpha}{cos\alpha}[/math][br][br][math]1+tg^2\alpha=\frac{1}{cos^2\alpha}=sec^2\alpha[/math]

Razones de la suma y diferencia de ángulos: [br] [math]sen\left(\alpha+\beta\right)=sen\alpha·cos\beta+sen\beta·cos\alpha[/math]    [math]sen\left(\alpha-\beta\right)=sen\alpha·cos\beta-sen\beta·cos\alpha[/math][br] [math]cos\left(\alpha+\beta\right)=cos\alpha·cos\beta-sen\alpha·sen\beta[/math] [math]cos\left(\alpha-\beta\right)=cos\alpha·cos\beta+sen\alpha·sen\beta[/math] [math]tg\left(\alpha+\beta\right)=\frac{tg\alpha+tg\beta}{1-tg\alpha·tg\beta}[/math]     [math]tg\left(\alpha-\beta\right)=\frac{tg\alpha-tg\beta}{1+tg\alpha·tg\beta}[/math][br][br]Razones del ángulo doble y mitad: [br] [math]sen\left(2\alpha\right)=2sen\alpha·sen\beta[/math]      [math]sen\left(\frac{\alpha}{2}\right)=\pm\sqrt{\frac{1-cos\alpha}{2}}[/math][br] [math]cos\left(2\alpha\right)=cos^2\alpha-sen^2\alpha[/math]     [math]cos\left(\frac{\alpha}{2}\right)=\pm\sqrt{\frac{1+cos\alpha}{2}}[/math] [br] [math]tg\left(2\alpha\right)=\frac{2tg\alpha}{1-tg^2\alpha}[/math]     [math]tg\left(\frac{\alpha}{2}\right)=\pm\sqrt{\frac{1-cos\alpha}{1+cos\alpha}}[/math]