Question

Check all that apply. cot 0 is undefined for 0=___?
1) pi/2
2) 0

4) 3pi/2

Answer 1

The cotangent function, cot θ, is undefined when the sine of the angle is zero. In the given options, cot θ is only undefined at θ = 0, since sin 0 = 0, making the division by zero undefined.

Step-by-step explanation:

To determine when the cotangent function, or cot θ, is undefined, we need to look at the definition of the cotangent as the ratio of the cosine of an angle to the sine of that angle, expressed as cot θ = cos θ / sin θ. The cotangent function will be undefined whenever the sine of the angle is zero, since division by zero is undefined in mathematics. It happens at integer multiples of π, where θ equals 0, π, 2π, 3π, etc. Specifically, for the angles provided in the question:

• π/2 - At this angle, sin θ is 1, so cot θ is well-defined here.
• 0 - Sin 0 is 0, so cot 0 is undefined at θ = 0.
• 3π/2 - At this angle, sin θ is -1, resulting in a well-defined cot θ.

Therefore, the only angle from the given options where cot θ is undefined is θ = 0.