Question #d07cf Trigonometry Right Triangles Trigonometric Functions of Any Angle 2 Answers P dilip_k Dec 11, 2016 #sin(-pi/12)# #=-sin(pi/12)# #=-sqrt(1/2(1-cos((2xxpi)/12)# #=-sqrt(1/2(1-cos(pi/6)# #=-sqrt(1/2(1-sqrt3/2)# #=-sqrt(1/8(4-2sqrt3)# #=-sqrt(1/8((sqrt3)^2+1^2-2sqrt3xx1)# #=-sqrt(1/8((sqrt3-1)^2)# #=-1/(2sqrt2)(sqrt3-1)# Answer link Bdub Dec 12, 2016 #(sqrt2-sqrt6)/4# Explanation: #sin(-pi/12) =sin(pi/6-pi/4)# Now use the formula #sin(A-B) =sin A cos B-cos A sin B# to evaluate #sin(pi/6-pi/4)#. That is, #sin(pi/6-pi/4)=sin (pi/6) cos (pi/4) - cos (pi/6) sin (pi/4)# #=1/2*sqrt2/2 - sqrt3/2*sqrt2/2# #=sqrt2/4-sqrt6/4# #:=(sqrt2-sqrt6)/4# 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 1415 views around the world You can reuse this answer Creative Commons License