Question

Show how to use the unit circle to find tan60

Answer 1

`\tan 60^(\circ)~\text{equals y coordinate divided by x coordinate, where }(x,y) = \left(\frac 12, \frac{\sqrt 3}2 \right)`

`\tan 60^(\circ)\\\\= \frac yx \\\\\\=(\sin 60^\circ)/(\cos 60^\circ)\\\\\\=\frac{\tfrac{\sqrt 3}2}{\tfrac 12}\\\\\\=\frac{\sqrt 3}2 * 2\\\\\\=\sqrt 3`

Answer 2

• tanA=y/x

This rule is enough

Now

• y=sinA
• x=cosA

Here A=60°

• tan60=sin60/cos60
• tan60=√3/2÷1/2
• tan60=√3