Question
Question 5 (2 points) Think About It: 1. Why is tan \( 90^{\circ} \) undefined? 2. What is the other angle on the unit circle where tangent is undefined?
Ask by Davey Medina. in the United States
Feb 25,2025
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Answer
1. Tan 90° is undefined because cosine of 90° is zero.
2. Tangent is also undefined at 270° on the unit circle.
Solution
1. Tan 90° is undefined because the tangent function is sinθ/cosθ, and at 90° the cosine is 0, which means you would be dividing by zero.
2. The other angle on the unit circle where tangent is undefined is 270°, since cos 270° is also 0.
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When we look at the tangent function, it's defined as the sine of an angle divided by the cosine of that angle. At \( 90^{\circ} \), the cosine is 0, meaning you're dividing by zero, which makes the value undefined. This quirky nature of trigonometric functions reminds us that some angles just have that rebellious streak! The other angle on the unit circle where tangent is also undefined occurs at \( 270^{\circ} \). Here too, the cosine of the angle is 0, leading to that dreaded division by zero scenario. So, both \( 90^{\circ} \) and \( 270^{\circ} \) keep tangent at bay, reminding us that some divides are just too dangerous!
