If sin theta = -15/17 and theta is in the fourth quadrant, what is sec theta? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Nghi N. May 28, 2016 #17/8# Explanation: Use the trig identity: #cos^2 x = 1 - sin^2 x# #cos ^2 t = 1 - sin^2 t = 1 - 225/278 = 64/278 # #cos t = 8/17# (in Quadrant 4, cos x is positive) #sec t = 1/(cos t) = 17/8# 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 9820 views around the world You can reuse this answer Creative Commons License