How do you find the remaining trigonometric ratios if #sec(theta) = -3.5# and #pi/2< theta < pi#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Nghi N. May 30, 2015 #sec x = 1/cos x = -3.5 -> cos x = 1/-3.5 = -0.286# #sin^2 x = 1 - (0.286)^2 = 0.92 -> sin x = 0.96# #tan x = 0.96/-0.286 = -3.36# #cot x = 1/ -3.36 = 0.30# #csc x = 1/(sin x) = 1/0.96 = 1.04# 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 11099 views around the world You can reuse this answer Creative Commons License