A sine is a fundamental trigonometric function that, in the context of a right triangle, is the ratio of the length of the side opposite a given angle to the length of the triangle’s hypotenuse. It is commonly denoted as sin(θ) for an angle θ. Key points:

• In a right triangle: sin(θ) = opposite / hypotenuse.
• It can be defined for any angle using the unit circle: sin(θ) is the y-coordinate of the point on the unit circle corresponding to angle θ.
• Basic identities: sin^2(θ) + cos^2(θ) = 1, sin(2θ) = 2 sin(θ) cos(θ), and the angle addition formula sin(α ± β) = sin(α)cos(β) ± cos(α)sin(β).
• The reciprocal of sine is cosecant: csc(θ) = 1 / sin(θ).
• Sine values are periodic with period 2π in radians (or 360° in degrees).

If you’d like, I can tailor a quick example problem to illustrate how to compute sin(θ) in a right triangle or on the unit circle.