Answer
$a=cot\theta$ and $b=csc\theta$
Work Step by Step
Step 1. Use the figure given in the Exercise, since side $a$ is parallel to the x-axis, the angel between $a$ and $b$ is also $\theta$
Step 2. Given the radius of the circle as 1, in the red triangle, by definition $sin\theta=\frac{1}{b}$ thus we have $b=\frac{1}{sin\theta}=csc\theta$
Step 3. In the same triangle, $tan\theta=\frac{1}{a}$, we have $a=\frac{1}{tan\theta}=cot\theta$
