Question

What is the exact value of tan 30° ? Enter your answer, as a simplified fraction, in the box.

Answer 1

hmmm if you don't have a Unit Circle, this is a good time to get one, many you can find online. Anyhow, check your unit circle for cos(30°) and sin(30°).


`\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad tan(30^o)=\cfrac{sin(30^o)}{cos(30^o)} \\\\\\ tan(30^o)=\cfrac{\quad (1)/(2)\quad }{(√(3))/(2)}\implies tan(30^o)=\cfrac{1}{2}\cdot \cfrac{2}{√(3)}\implies tan(30^o)=\cfrac{1}{√(3)} \\\\\\ \stackrel{\textit{and now if we rationalize the denominator}}{\cfrac{1}{√(3)}\cdot \cfrac{√(3)}{√(3)}\implies \cfrac{√(3)}{(√(3))^2}\implies \cfrac{√(3)}{3}}`