نسبت‌های مثلثاتی در مرزها: $\sin(0^{\circ}) = 0, \quad \cos(0^{\circ}) = 1, \quad \tan(0^{\circ}) = \frac{\sin}{\cos} = \frac{0}{1} = 0, \quad \cot(0^{\circ}) = \frac{\cos(0^{\circ})}{\sin(0^{\circ})} = \frac{1}{0}$ $\sin(90^{\circ}) = 1, \quad \cos(90^{\circ}) = 0, \quad \tan(90^{\circ}) = \frac{1}{0}, \quad \cot(90^{\circ}) = \frac{0}{1} = 0$ $\sin(180^{\circ}) = 0, \quad \cos(180^{\circ}) = (-1), \quad \tan(180^{\circ}) = \frac{0}{-1} = 0, \quad \cot(180^{\circ}) = \frac{1}{0}$ $\sin(270^{\circ}) = (-1), \quad \cos(270^{\circ}) = 0, \quad \tan(270^{\circ}) = \frac{-1}{0}, \quad \cot(270^{\circ}) = \frac{0}{-1} = 0$ $\sin(360^{\circ}) = 0, \quad \cos(360^{\circ}) = 1, \quad \tan(360^{\circ}) = \frac{\sin}{\cos} = \frac{0}{1} = 0, \quad \cot(360^{\circ}) = \frac{\cos}{\sin} = \frac{1}{0}$ [شکل: دایره مثلثاتی با برچسب زوایای 0، 90، 180، 270 درجه و محورهای سینوس و کسینوس]