UNIT 5 : TRI60NOMETRY ' '

,, 22 Trigonometrical Ratios

POINT$ TO lEMEMBEl 1. Trigonometrical Ratios (T-Ratios) of An Angle

In MBC, let LB = 90 and let LA be acute. For LA, we have

Base = AB, Perp. = BC and Hyp. = AC. The T-ratios for LA are defined as :

(i) Sine A Perp. = BC , written as sin A. Hyp. AC

(ii) Cosine A = Base = AB , written as cos A. Hyp. AC

(iii) Tangent A = Perp. = BC , ~itten as tan A. Base AB

(iv) Cosecant A = Hyp. = AC, written as cosec A. Perp. BC

(v) Secant A = Hyp. = AC, written as sec A. Base AB

(vi) CotangentA = Base = AB, written as cot A. Perp. BC

2. Reciprocal Relations :

(i) cosec A = . 1 SID A

Thus, we have :

(ii) sec A = 1 cos A

(i) sin A cosec A = 1 (ii) cos A sec A = 1 3. Quotient Relations in T-Ratios

sine (i) =tan e cos e

cos e ( ") =cot e 11 e Sin

c

Perp.

,

( ... ) A 1 111 cot = --tan A

,

(iii) tan A cot A= 1.