Trigonometry at a Glance: Key Formulas and Identities, Cheat Sheet of Mathematics

Download Trigonometry at a Glance: Key Formulas and Identities and more Cheat Sheet Mathematics in PDF only on Docsity! TRIGONOMETRY AT A GLANCE Trigonometric ra�o’s in right angled triangle: Cosec O S H Sin Sec A C H Cos Cot O T A Tan Reverse 4k 5k B A C By Pythagorean theorem 3k = (5k)2 - (4k)2 √ 4 5 O H 4k 5kSin C = = = A H 3 5 3k 5kSos C = = = O A 4 3 4k 3kTan C = = = A O 3 4 3k 4kCot C = = = H A 5 3 4k 3kSec C = = = H O 5 3 4k 3kCosec C = = = If Sin A = 4 5 , then tan θ sin θ cos θ sec θ cosec θ cosec θ sec θ cosec θ cot θ 1 cot θ 1 tan θ 1 cos θ 1 sin θ cos θ sin θ tan θ x cosec θ sec θ x cot θ sec θ tan θ cot θ sec θ cosec θ Trigonometric ra�os of standard angles: Standard Angles (θ) 0º 0 1 2 3 4 30º 45º 60º 90º 0 4 = 0 4 4 = 11 4 3 4 2 4 1 2= sin θ cos θ tan θ cot θ sec θ cosec θ 1 1 1 1 1 2 2 Not define Not define Not define Not define 0 0 0 1 4 1 2= 1 2 1=√2 3 4 2=√3√0 = 0 √1 = 1 1 22 √3 1 √2 1 √3 2 √3 2 √3 1 √3 √3 √3 √2 √2 Write numbers from 0 to 4. Divide all by 4. Find square root . Write the values in reverse order. Write the values in reverse order. Write the values in reverse order. Use: tan θ = sin θ cos θ Use: tan θ = sin θ cos θ Sine and Cosine are complementary of each other. sin (90° − θ) = cos θ and cos (90° − θ) = sin θ. Tangent and Cotangent are complementary of each other. tan (90° − θ) = cot θ and cot (90° − θ) = tan θ. Secant and Cosecant are complementary of each other. cosec (90° − θ) = sec θ and sec (90° − θ) = cosec θ. Rela�on among trigonometric ra�o’s: Trigonometric ra�o of complementary angles: Remember “OSHACHOTA”. sin θ = y r sin2 θ = y2 r2 sin θ = x r sin2 θ + cos2 θ sin2 θ = x2 r2 y2 r2 x2 r2 y2 + x2 r2= =+ r2 r2= = 1 [By Pythagorean theorem] sin2 θ + cos2 θ = 1 sec2 θ - tan2 θ = 1 cosec2 θ - cot2 θ = 1 Similarly, Identities sin2 θ + cos2 θ = 1 sec2 θ - tan2 θ = 1 cosec2 θ - cot2 θ = 1 1 + cos2 θ = sin2 θ 1 + tan2 θ = sec2 θ 1 + cot2 θ = cosec2 θ 1 - sin2 θ = son2 θ sin2 θ -1 = tan2 θ cosec2 θ -1 = cot2 θ Iden��es: A B C y r x θ