\( 0 / 2 \) Question 5 Think About It: 1. Why is tan \( 90^{\circ} \) undefined? - 2. What is the other angle on the unit circle where tangent is undefined? - Think About It: 1. Why is tan \( 90^{\circ} \) undefined? X division by zero 2. What is the other angle on the unit circle where tangent is undefined? \( X \underline{270 \text { degree }} \)

Let's break down the questions regarding the tangent function and its behavior on the unit circle. ### 1. Why is \(\tan 90^{\circ}\) undefined? The tangent function is defined as the ratio of the sine and cosine functions: \[ \tan \theta = \frac{\sin \theta}{\cos \theta} \] At \(90^{\circ}\): - \(\sin 90^{\circ} = 1\) - \(\cos 90^{\circ} = 0\) Thus, we have: \[ \tan 90^{\circ} = \frac{1}{0} \] Division by zero is undefined in mathematics, which is why \(\tan 90^{\circ}\) is considered undefined. ### 2. What is the other angle on the unit circle where tangent is undefined? The tangent function is also undefined at \(270^{\circ}\) for similar reasons. At \(270^{\circ}\): - \(\sin 270^{\circ} = -1\) - \(\cos 270^{\circ} = 0\) Thus, we have: \[ \tan 270^{\circ} = \frac{-1}{0} \] Again, division by zero occurs, making \(\tan 270^{\circ}\) undefined. ### Summary - \(\tan 90^{\circ}\) is undefined because it involves division by zero. - The other angle on the unit circle where tangent is undefined is \(270^{\circ}\).