## 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 a series of which the first term is θ and succeeding terms alternate in sign with the

*k*th term being a fraction whose numerator consists of θ raised to the exponent 2

*k*- 1 and whose denominator is the factorial of 2

*k*- 1