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.                                                                                                                                                                                                                                                                                                                                                                                                                                         cos[n • 360°]

Accepted Answer

Welcome back. I am so glad you're here. We're asked to identify if the given expression is undefined, equal to 01 or negative. One note that N is either a positive or negative integer. Our expression is the cosigned of 180 degrees plus N multiplied by 360 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 let's look at our expression. So we could choose some different values for N, we note that N is either a positive or a negative integer. So we could use an N value of one. And what would that give us? So we'd have the cosine of open bracket, 180 degrees plus one multiplied by 360 degrees and one multiplied by degrees is 360 degrees. So we've got the cosine of 180 degrees plus 360 degrees and 180 degrees plus 360 degrees is 540 degrees. So we have the cosine of 540 degrees. And if we wanted to find that angle between zero and 360 degrees, we could take away one full rotation, subtracting 360 degrees. And that would just bring us right back to the cosine of 180 degrees. No matter what we choose for our end values, we're going to have angles that are co terminal with 180 degrees. So really the question that we're asking ourselves is what's the cosine of 180 degrees? And we recall from previous lessons and from the tables in the book, this is a quadrant angle and from those tables in the book, the cosine of 180 degrees is equal to negative one. And so no matter what we put in for N there we are going to get negative one, we look at our answer choices and that matches with answer choice. D 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. cos[n • 360°]

Key Concepts

Periodic Functions

Cosine Function Values

Integer Multiples of Angles

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