Give an expression that generates all angles coterminal with a...

Question

Give an expression that generates all angles coterminal with an angle of π/6 radian. Let n represent any integer.

Accepted Answer

Welcome back. I am so glad you're here. We are asked to write an expression that represents all angles that are co terminal with seven pi divided by 13 radians. Let any integer be represented by K. Our answer choices are answer choice. A seven pi divided by 13 plus three K pi answer choice B seven pi divided by 13 plus two K pi answer choice C seven pi divided by 13 plus K pi divided by two and answer choice. D seven pi divided by 13 plus three K pi divided by two. All right. So we've got the angle seven pi divided by 13 radiant and we want all of its co terminal angles. So that means angles that have gone at least once, all the way around the circle. So how do we represent one rotation, one full rotation, all the way around a circle in radiance, one full rotation, all the way around a circle in radiance is two pi. And so we'll be adding to pie to our seven pi divided by 13, but that only gets us around once. What if we want to go around twice? Is that also co terminal? Yes, it is. So we could multiply our two pi by two or we could go around three times, we can multiply two pi by three that can just keep going. Now, what if we wanted to go in the negative direction? If we went all the way around once in the negative direction, would that be co terminal? Yes, it would. So we can multiply our two pi by negative one or we could go around twice, multiply our two pi by negative two that can keep going as well. And we're going to represent all of those different integers, 23, negative one, negative two and so on by K. So we're going to multiply our two pi by OK. And we can rewrite this part two pi multiplied by K in the way that we traditionally write these, we put two, our number K, our variable and then pi and then that's being added to seven pi divided by 13. That is the expression that represents all angles that are co terminal with seven pi divided by 13 radiance. We look at our answer choices for seven pi divided by 13 plus two K pi and that matches with answer choice B well done. We'll catch you on the next one.

Give an expression that generates all angles coterminal with an angle of π/6 radian. Let n represent any integer.

Key Concepts

Coterminal Angles

Radians

Integer Representation

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