# CLASS-9TRIGONOMETRICAL RATIOS - T-RATIOS OF AN ANGLE

Trigonometrical Ratios (T-Ratios) of an Angle

In ABC, let ∠B = 90⁰ and let ∠A be acute.

For ∠A, we have –

Base = AB, Perpendicular = BC, and Hypotenuse = AC. The T-ratios for ∠A are defined as –

Perpendicular         BC

(iSine = --------------- = -------, written as  sin A

Hypotenuse          AC

Base              AB

(ii) Cosine A = -------------- = -------, written as cos A

Hypotenuse          AC

Perpendicular           BC

(iii) Tangent A = ---------------- = -------, written as tan A

Base                 AB

Hypotenuse           AC

(iv) Cosecant A = ---------------- = -------, written as cosec A

Perpendicular          BC

Hypotenuse          AC

(v) Secant A = -------------- = -------, written as sec A

Base              AB

Base               AB

(vi) Cotangent A = --------------- = -------, written as cot A

Perpendicular         BC

Thus, the six trigonometrical ratios for an acute angle θ of a right triangle can be defined as –

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