How do I find the exact value of this trigonometric function?? I know y/x but how do I simplify it?

Question

tan5(*pie symbol)/ 6 

 

 

Answer 1

tan5∏/6

∏=180º

tan 5*30º

tan 150º or simply look for 5∏/6 on the unit circle and you find (-√3/2, 1/2)

on the unit circle the coordinates are (cosθ, sinθ)

tan=sin/cos

tan=(1/2)/(-√3/2)

tan=(1/2)*(2/-√3)

tan=1/-√3

multiply both terms by √3

tan=(1*√3)/[-√3]*[√3]

tan=-√3/3 (the minus sign can be in the numerator or the denominator)