How do you determine #costheta# given #sintheta=-1/5,pi<theta<(3pi)/2#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Binayaka C. Sep 11, 2017 #cos theta= -(2sqrt6)/5# Explanation: #theta# is in 3rd quadrant where both #sin theta and cos theta # is negative. # sin theta = 1/-5 :. sin^2 theta = 1/25 # # cos theta = +-sqrt(1-sin^2 theta) = +-sqrt (1-1/25) =+-sqrt 24/5# Since #cos theta # is negative in 3rd quadrant , # cos theta= -sqrt 24/5 or cos theta= -(2sqrt6)/5# [Ans] 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 7299 views around the world You can reuse this answer Creative Commons License