Given #sin theta = (-12/13)#, and #cos theta > 0#, how do you find the exact values of sin(2theta) and cos(2theta)? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Shwetank Mauria Mar 5, 2017 #sin2theta=-120/169# and #cos2theta=-119/169# Explanation: As #sintheta=-12/13# i.e. negative and #costheta# is positive, #theta# lies in #Q4# i.e. #(3pi)/2< theta < 2pi# #costheta=sqrt(1-(-12/13)^2)-sqrt(1-144/169)=sqrt(25/169)=5/13# Hence, #sin2theta=2sinthetacostheta=2xx(-12/13)xx5/13=-120/169# and #cos2theta=cos^theta-sin^2theta=25/169-144/169=-119/169# 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 9741 views around the world You can reuse this answer Creative Commons License