A V B The Eight Fundamental Identities Basic Identities Common Equivalent Forms 1 CSCO = 1 sin 0 sin 8 = csc 0 Reciprocal sec 8 = cos e cos 0 = sec. 0 cot 0 = tan 0 tan 0 = cote sin 0 tan 0 = sine = cos 0 tan 0 Ratio or Quotient cos 0 cos e cot 0 = cos 0 = sin 0 cot 0 sin 0 cost0 + sin-0 = 1 sin20 = 1 - cos20 1 + tan 0 = sec20 sin 0 = +v1 -cos2 0 Pythagorean cos20 = 1 - sin20 1 + cot20 = csc20 cos 0 = #v1 - sin20EXERCISES 1 Find the value of trigonometric function given the value of its reciprocal. 1. If csc 0 = -, find sin 0. 2. If sec 0 = , find cos 0. 3. If tan 0 = find cot 0. 4. If sin 0 = 5 find csco. 5. If sin 0 = -2, find csco.Find the value of each expression using the given information. 1. If cos x = = and sin x = V35 6 6 , find cot x. 2. Find tan 0 if sin 0 = UT I W and cos 0 = - UTI 3. Find cot 0 if sin 0 = - > and cos 12 13 4. Find sec x = 2 and tan x = V3, find sin x. 5. If csc x = - and cot x = 2V10 3 find sec x.EXERCISES 4 Write each of the following in terms of sin 0 and cos 0, and then simplify if possible. 1. cos 0 cot 0 2. csc 0 tan 0 3. sec 8 CSC 8 sin 0 4. csce 5. sec 0 tan 0 csc 0