How do you prove #Cos(x-(3pi)/2)=-sinx#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer sente Feb 12, 2016 Using the identities #cos(x-pi/2) = sin(x)# #sin(x-pi/2) = -cos(x)# We have: #cos(x-(3pi)/2) = cos((x-pi)-pi/2)# #=sin(x-pi)# #=sin((x-pi/2)-pi/2)# #=-cos(x-pi/2)# #=-sin(x)# Answer link Related questions How do you find the trigonometric functions of any angle? What is the reference angle? How do you use the ordered pairs on a unit circle to evaluate a trigonometric function of any angle? What is the reference angle for #140^\circ#? How do you find the value of #cot 300^@#? What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#? How do you know if #sin 30 = sin 150#? How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle Impact of this question 10453 views around the world You can reuse this answer Creative Commons License