In Exercises 57–70, find a positive angle less than or that is...

Question

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. - 38𝜋/9

Accepted Answer

Welcome back. I am so glad you're here. We're told, given the angle negative 30 pi divided by seven, identify a positive co terminal angle less than two pi. Our answer choices are answer choice. A 11 pi divided by seven. Answer choice B 13 pi divided by seven answer choice C 10 pi divided by seven and answer choice D 12 pi divided by seven. All right. So we've got this negative angle. We want to find a positive co terminal one but we can't go any further than two pi. So we want to get closer to two pi, we're going to add full rotations. We're going to add two pies to this until we get between zero and two pi. But what is two pi when we have a denominator of seven? So if we wanna add two pi, we need a denominator of seven. So we're going to take our two pi and multiply it by seven divided by seven, which will give us a numerator of 14 pi and then divide it by seven. And now we can add that to our negative 30 pi divided by seven. So adding our numerators negative 30 pi plus pi brings us to negative 16 pi divided by seven. Is that in between zero and two pi not yet. So we'll add another full rotation. Another 14 pi divided by seven adding our numerators, negative 16 pi plus 14 pi gets us close. It gets us to negative two pi divided by seven, but we're not between zero and two pi yet. So we'll add another 14 pi divided by seven going around the circle again. And now negative two pi plus 14 pi brings us to 12 pie divided by seven. And that is between zero and two pi. We know that two pi would be 14 pi divided by seven. So there's our co terminal angle that meets those requirements. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. - 38𝜋/9

Key Concepts

Coterminal Angles

Angle Measurement in Radians

Modulo Operation with Angles

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