How do you find the exact values of the remaining five trigonometric functions of angle, given csc of the angle is -4? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Nghi N. May 17, 2015 #csc x = 1/sin x = -4 -> sin x = -1/4# #cos^2 x = 1 - sin^2 x = 1 - 1/16 = 15/16 -> cos x = +- sqrt15/4# #tan x = - (1/4) (4/(sqrt15)) = (-sqr15)/15# #cot x = -15/(sqrt15) = (-15sqrt15)/15 = -sqrt15 # #sec x = 1/cos x = -4/(sqrt15)# = #-(4sqrt15)/15# Answer link Related questions What does it mean to find the sign of a trigonometric function and how do you find it? What are the reciprocal identities of trigonometric functions? What are the quotient identities for a trigonometric functions? What are the cofunction identities and reflection properties for trigonometric functions? What is the pythagorean identity? If #sec theta = 4#, how do you use the reciprocal identity to find #cos theta#? How do you find the domain and range of sine, cosine, and tangent? What quadrant does #cot 325^@# lie in and what is the sign? How do you use use quotient identities to explain why the tangent and cotangent function have... How do you show that #1+tan^2 theta = sec ^2 theta#? See all questions in Relating Trigonometric Functions Impact of this question 3299 views around the world You can reuse this answer Creative Commons License