How do you use the half angle identity to find exact value of tan3pi/8?

Question

1558 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-02T22:25:15

Refer to explanation

The half angle formula for tangent can be written as follows

$tan(theta/2)=(1-costheta)/sintheta$

So we'll try applying the half angle formula for tangent using $theta=(3pi)/4$ hence we have that

$tan((3pi)/8)=((1-cos((3pi)/4))/sin((3pi)/4))$

Using the unit circle, we can see that

$sin((3pi)/4)=sqrt2/2$ , $cos((3pi)/4)=-sqrt2/2$

So we substitute in the previous equation we get

$tan((3pi)/8)=1+sqrt2$