If n is an integer, n • 180° represents an integer multiple of 1...

Question

If n is an integer, n • 180°  represents an integer multiple of 180°, (2n + 1) • 90°  represents an odd integer multiple of 90° ,  and so on. Determine whether each expression is equal to 0, 1, or  ―1, or is undefined.                                                                                                                                                                                                                                                                                                                                                                                                                                          cot[n • 180°]

Accepted Answer

Welcome back. I am so glad you're here. We are asked to identify if the given expression is undefined equal to 01 or negative. One note that N is either a positive or a negative integer. Our given expression is the tangent of open bracket N multiplied by 180 degrees. Our answer choices are answer choice, a undefined answer, choice B zero, answer choice C one and answer choice D negative one. All right. So for N, we can choose either a positive or a negative integer. So let's start with a positive one. I'm plugging one, N for N. So we're taking the tangent of one multiplied by 180 degrees. So we're looking for the tangent of one multiplied by 180 degrees, which is 180 degrees. So we're looking for the tangent of 180 degrees. And we know from previous lessons and from the tables in the book that the tangent of 180 degrees is equal to zero. And so if we chose different values for N, let's say we have an N value of two plugging that in we have the tangent of two multiplied by 180 degrees. Well, two multiplied by 180 degrees is 360 degrees. So here we're looking at the tangent of 360 degrees and that's also a quadrant angle. And we have those tables in the book and that also tells us that the tangent of 360 degrees is zero as well. Now, if we have 180 degrees or 360 degrees, any other numbers that we choose for? N we're just going to be getting co terminal angles with 180 degrees or 360 degrees. So no matter what, here we are going to be getting an answer of zero, we look at our answer choices and that matches with answer choice. B well done. We'll catch you on the next one.

If n is an integer, n • 180° represents an integer multiple of 180°, (2n + 1) • 90° represents an odd integer multiple of 90° , and so on. Determine whether each expression is equal to 0, 1, or ―1, or is undefined. cot[n • 180°]

Key Concepts

Cotangent Function

Integer Multiples of Angles

Trigonometric Values at Key Angles

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