How do you evaluate #sin(( 7pi) / 2)#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer maganbhai P. Apr 15, 2018 #sin((7pi)/2)=-1# Explanation: We know that, #color(red)(sin(3pi+theta)=-sintheta# Here, #sin((7pi)/2)=sin((6pi+pi)/2)# #=sin(3pi+pi/2)...toIII^(rd) Quadrant, where, sin is -ve# #=-sin(pi/2)# #=-1# Note: #(1)theta=pi/2,(5pi)/2,(9pi)/2,(13pi)/2...=>sintheta=1# #(2)theta=(3pi)/2,(7pi)/2,(11pi)/2,(15pi)/2...=>sintheta=-1# 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 32071 views around the world You can reuse this answer Creative Commons License