Definition: Trigonometric Ratios

In a right-angled triangle, trigonometric ratios relate angles and sides. The primary ratios are sine (sin), cosine (cos), and tangent (tan).

Explanation:

Trigonometric ratios are mathematical relationships that exist between the angles and sides of a right-angled triangle.

These ratios express the connections between the lengths of specific sides and the measures of particular angles in the triangle.

Simply put, trigonometric ratios are a set of rules that relate the angles and sides of a right-angled triangle to each other.

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\$.