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.                                                                                                                                                                                                                                                                                                                                                                                                                                         sin[270° + 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 sign of 180 degrees plus N multiplied by 360 degrees. Our answer choices are answer choice. A zero answer. Choice. B one answer, choice, C negative one and answer choice D undefined. All right, let's pick some different values for N. If we choose an N value of one, substituting that N for N, we've got the sign of open bracket degrees plus one multiplied by degrees. One multiplied by 360 degrees is 360 degrees. So we have the sign of 180 degrees plus 360 degrees and 180 degrees plus 360 degrees is 540 degrees. So we have the sign of 540 degrees. And if we wanted that to be within between zero and 360 degrees, we take that 540 subtract a full rotation. So 360 degrees and 540 degrees minus 360 degrees brings us right back to that 180 degrees. So here we're taking the sign of 180 degrees. We recall from previous lessons and from the tables in the book that the sign of 180 degrees, that quadrant angle is zero. Now, if we chose any other number for N, we would just be multiplying it more times more rotations around in a circle. We'd just be getting co terminal angles with 180 degrees. So no matter what we choose for our N, we would end up with the sign of 180 degrees, which will be zero every time we'll look at our answer choices and this matches with answer choice. A 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. sin[270° + n • 360°]

Key Concepts

Periodic Functions

Sine Function Values

Angle Addition

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