## Definition of sine

**:**the trigonometric function that for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse

**:**a trigonometric function sin θ that for all real numbers θ is exactly equal to the sine of an angle of measure θ in radians and that is given by the sum of the alternating series {latex}\sin \theta = \theta - \frac{\theta^{3}}{3!} + \frac{\theta^{5}}{5!} - \frac{\theta^{7}}{7!} + \frac{\theta^{9}}{9!} - \dots{/latex}