Question #7c973 Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Nghi N Mar 1, 2017 #sin^2 t + 2# Explanation: #f(t) = 3sin^3 t.csc t + 2cos (-t).cos t# Because #csc t= 1/(sin t)# and #cos (-t) = cos t#, then: #f(t) = 3 sin^3 t(1/(sin t)) + 2cos^2 t = 3sin^2 t + 2cos ^2 t =# #f(t) = sin^2 t + 2(sin^2 t + cos^2 t) = sin^2 t + 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 1142 views around the world You can reuse this answer Creative Commons License