How do you determine #cottheta# given #csctheta=sqrt11/3,pi/2<theta<pi#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer maganbhai P. Jul 12, 2018 #cot theta=-sqrt2/3# Explanation: Here, #csctheta=sqrt11/3# Where, #pi/2 < theta < pi=>II^(nd)Quadrant=>color(red)(cot theta <0# We know that , #csc^2theta-cot^2theta=1# #=>cot^2theta=csc^2theta-1=11/9-1=2/9# #=>cot^2theta=(sqrt2/3)^2 # #=>cot theta=-sqrt2/3to[because color(red)(cottheta < 0)]# 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 2376 views around the world You can reuse this answer Creative Commons License