Definition: Sine (sin θ)

The ratio of the opposite side (to the angle) over the hypotenuse (longest side).

Explanation:

The sine of an angle in a right-angled triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In a unit circle, the sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle.

Definition: Cosine (cos θ):

The ratio of the adjacent side (closest to the angle) over the hypotenuse.

Explanation:

The cosine of an angle in a right-angled triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.

In a unit circle, the cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle.

Definition: Tangent (tan θ):

The ratio of the opposite side over the adjacent side.

Explanation:

The tangent of an angle in a right-angled triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

In a unit circle, the tangent of an angle is the ratio of the sine to the cosine of that angle, i.e., \$tan θ = sin θ / cos θ\$.