Trigonometrical Ratios
2
UNIT 5 : TRI60NOMETRY Trigonometrical atios POINT TO lEMEM El 1. Trigo nomet rical Ratios T-Ratios) of An Angle In MBC let LB = 90° and let L A be acute. For L A we have Base = AB, Perp. = BC and Hyp. = AC. The T-ratios for L A ar e 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 , i t t n 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 = . SID A Thus, we have : ii) sec A = cos A i) sin A cosec A = 1 ii) cos A sec A = 1 3. Quot ien t Relations in T-Ratios sine i) =tan e cos e cos e ) =cot e • e Sin c Perp. , ( ) A 1 cot = tan A , iii) tan A cot A= 1.
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Basic Trigo from Arun Deep's
Transcript of Trigonometrical Ratios
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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.
