Trigonometry is the study of relationships between the sides and angles of triangles, especially right triangles.

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

Tangent of an angle is the ratio of the length of the opposite side to the adjacent side in a right triangle.

sin A = (length of opposite side) / (length of hypotenuse)

cos A = (length of adjacent side) / (length of hypotenuse)

tan A = (length of opposite side) / (length of adjacent side)

Cosecant (csc A) is the reciprocal of sine: csc A = 1/sin A.

Secant (sec A) is the reciprocal of cosine: sec A = 1/cos A.

Cotangent (cot A) is the reciprocal of tangent: cot A = 1/tan A.

A right triangle has one angle measuring 90 degrees.

These angles have specific sine, cosine, and tangent values that are frequently used in calculations.

If one ratio is known, you can use the relationships between ratios to find the others.

The Pythagorean identity states sin²A + cos²A = 1 for any angle A.

sin 0° = 0

cos 0° = 1

tan 45° = 1

sin A = cos (90° - A) and cos A = sin (90° - A).

Trigonometric ratios are the ratios of the lengths of the sides of a right triangle corresponding to its angles.

Confusing sine, cosine, and tangent, or not distinguishing between angle measures and side lengths.

tan A = sin A / cos A and cot A = cos A / sin A.