How do you find the value of #sec theta# given #tan theta=3/2# and in quadrant III? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Ratnaker Mehta Aug 8, 2017 # -sqrt13/2.# Explanation: #sec^2theta=1+tan^2theta=1+(3/2)^2=1+9/4=13/4.# # sectheta=+-sqrt13/2.# Since, #theta# lies in #Q_(III), sectheta=-sqrt13/2.# 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 16873 views around the world You can reuse this answer Creative Commons License