Express #sin(x-(3pi)/4)# as a function of #sinx#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Shwetank Mauria Jan 31, 2018 #sin(x-(3pi)/4)=-1/sqrt2(sinx+sqrt(1-sin^2x))# Explanation: #sin(A-B)=sinAcosB-cosAsinB# Hence #sin(x-(3pi)/4)# = #sinxcos((3pi)/4)-cosxsin((3pi)/4)# = #sinx*-1/sqrt2-cosx*1/sqrt2# = #-1/sqrt2(sinx+cosx)# = #-1/sqrt2(sinx+sqrt(1-sin^2x))# 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 1130 views around the world You can reuse this answer Creative Commons License