1 1 1 2 2 2 3 3 4 3 4 5 6 TRIGONOMETRY Sides of Right-Angled Triangle Relations In Trigonometric Ratios Trigonometric Ratios Of Complementary Angles Trigonometric Ratios Of Standard Angles Here ND is not defined Trigonometric Identities In right-angled ΔABC, FA is an acute angle, AC is the hypotenuse, BC is the side opposite to FA, AB is the side adjacent to FA. sin 2 A + cos 2 A = 1 1 - cos 2 A = sin 2 A 1 - sin 2 A = cos 2 A N N 1+ tan 2 A = sec 2 A sec 2 A - tan 2 A = 1 sec 2 A - 1 = tan 2 A N N 1+ cot 2 A = cosec 2 A cosec 2 A - cot 2 A = 1 cosec 2 A - 1 = cot 2 A N N 1 cos A = tan A x cosec A = cot A cosec A sec A = 1 sin A = cot A x sec A = tan A sec A Cosec A = Angle 0 o 0 1 2 3 4 1 0 30 o 45 o 60 o 90 o Ratio 1 4 1 2 3 4 1 0 sin A 1 2 1 2 √ 3 2 √ 1 0 cos A 3 2 √ 1 2 √ 1 2 1 ND 0 tan A 3 √ 1 3 √ 1 ND 0 cot A 3 √ 1 3 √ 1 2 ND cosec A 2 √ 2 3 √ 2 ND 1 sec A 2 √ 2 3 √ Write values in reverse order Find square root for all write numbers from 0 to 4 Divide all by 4 Write values in reverse order Write values in reverse order Use sec A = 1 cos A Use tan A = sin A cos A sin A cos A cosec A sec A = = tan A = 1 cot A sin A cos A cosec A sec A cot A = = = 1 tan A sin (90-A) = cos A cos (90-A) = sin A tan (90-A) = cot A cot (90-A) = tan A sec (90-A) = cosec A cosec (90-A) = sec A sine and cosine are complementary to each other tangent and cotangent are complementary to each other cosecant and secant are complementary to each other 1 2 3 4 5 6 Sine of FA = sin A = = hypotenuse opposite side BC AC Cosine of FA = cos A = = hypotenuse adjacent side AB AC Tangent of FA = tan A = = opposite side adjacent side BC AB Cotangent of FA = cot A = = opposite side adjacent side BC AB Secant of FA = sec A = = hypotenuse adjacent side AC AB Cosecant of FA = cosec A = = hypotenuse opposite side BC AC Trigonometric Ratios Of A A Side adjacent to FA Hypotenuse Side opposite to FA B C