How do you find the exact values of #costheta# and #tantheta# when #sintheta=-2/3#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Nghi N · Shwetank Mauria Dec 30, 2016 #costheta= +- sqrt5/3# and #tantheta=+- (2sqrt5)/5# Explanation: Use trig identity: #cos^2 theta = 1 - sin^2 theta# #cos ^2theta = 1 - 4/9 = 5/9# #cos theta = +- sqrt5/3# #tan theta = sintheta/(cos theta) = +- (2/3)(3/sqrt5) = +- 2/sqrt5 = +- (2sqrt5)/5# 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 1218 views around the world You can reuse this answer Creative Commons License