How do you find the exact value of tan ( (3pi)/4)?

1 Answer
Jul 9, 2016

Since tan(theta) = (sin(theta))/(cos(theta))

tan((3pi)/(4))=sin((3pi)/(4)) / cos((3pi)/(4))

Knowing the unit circle, we can see that

sin((3pi)/(4)) = (sqrt(2))/(2)

and

cos((3pi)/(4)) = -(sqrt(2))/(2)

so

tan((3pi)/(4))=(((sqrt(2))/(2)) * (-2/sqrt(2))) / cancel(((-(sqrt(2))/(2))* (-2/sqrt(2))))

tan((3pi)/(4))=(-2*cancel(sqrt(2)))/(2*cancel(sqrt(2))) =-2/2=-1