Answer
$\frac{\sqrt 3}{2}$, $ \frac{1}{2}$, $ \sqrt 3$, $ \frac{\sqrt 3}{3}$, $ 2$, and $ \frac{2\sqrt 3}{3}$.
Work Step by Step
Given $\theta=420^\circ=360^\circ+60^\circ$ (quadrant I), we have $sin\theta =sin60^\circ=\frac{\sqrt 3}{2}$, $cos\theta =cos60^\circ=\frac{1}{2}$, $tan\theta =tan60^\circ=\sqrt 3$, $cot\theta = \frac{1}{tan\theta}=\frac{\sqrt 3}{3}$, $sec\theta = \frac{1}{cos\theta}=2$, and $csc\theta = \frac{1}{sin\theta}=\frac{2\sqrt 3}{3}$.
