Final answer:
The six trigonometric ratios associated with an angle in a triangle are sine, cosine, tangent, cosecant, secant, and cotangent.
Step-by-step explanation:
The six trigonometric ratios associated with an angle in a triangle are the following:
- Sine (sin): The ratio of the opposite side to the hypotenuse of the triangle. It is calculated as sin(A) = opposite/hypotenuse.
- Cosine (cos): The ratio of the adjacent side to the hypotenuse of the triangle. It is calculated as cos(A) = adjacent/hypotenuse.
- Tangent (tan): The ratio of the opposite side to the adjacent side of the triangle. It is calculated as tan(A) = opposite/adjacent.
- Cosecant (csc): The reciprocal of the sine. It is calculated as csc(A) = hypotenuse/opposite.
- Secant (sec): The reciprocal of the cosine. It is calculated as sec(A) = hypotenuse/adjacent.
- Cotangent (cot): The reciprocal of the tangent. It is calculated as cot(A) = adjacent/opposite.