How do you find the exact value of #sin690#? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Ratnaker Mehta Jul 26, 2018 # -1/2#. Explanation: #sin690^@=sin(720^@-30^@)#, #=sin(4pi-pi/6)#. But, #sin(4pi-theta)=-sintheta#. #:. sin690^@=-sin30^@=-1/2#. 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 12665 views around the world You can reuse this answer Creative Commons License