In Exercises 87–90, find the absolute value of the radian measure...

Question

In Exercises 87–90, find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time.

55 seconds

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the angle in radiance at which the second hand of a clock rotates through the following time. We are to consider the clockwise rotation as positive. Our time is at 42 seconds. Our answer choices are answer choice. A four pi divided by three answer choice B 16 pi divided by 15 answer trace C seven pi divided by five and answer choice D 14 pi divided by 15. All right. So we're talking about a clock. We are not talking about our standard position for an angle. We've got a clock specifically, we're talking about the second hand of a clock. So the initial side for a, an angle that has to do with the clock from the center, it's pointing up toward 12 o'clock straight up. And what we need to determine is where is that terminal side after 42 seconds? But in radiance, well, as we're talking about clockwise rotation from our initial side as we had clockwise. Now, this time, it's positive. If we were to make one full rotation, we're talking about seconds. How many seconds is that? Well, that full rotation is at 60 seconds, but we've only got 42 of those seconds. Well, we can set that up as a ratio. So 42 is in our numerator. That's how far we've gone. That's divided by 60. What would be one complete rotation? That's our base. But we need to convert this to radiant. So we've set that equal to another fraction for our ratio. Well, what's the base in radiance or in other words, what's one complete rotation in radians? And we recall from previous lessons that that is two pi when we're talking about radians. So that's our base. That's our denominator for the fraction on the right hand side of the equal sign. And how about, how far have we gone? Well, that's what we're trying to find out. So we can put an X in our numerator. Now, we just need to solve for X and that will give us our answer ingredients to solve for X. We multiply both sides of our equation by two pi. So on the left hand side in the numerator, we have two pi multiplied by 42 that's divided by 60. And we simplify that, that will be seven pi divided by five. And that is our angle in radiant. We look at our answer choices and this matches with answer choice. See well done. We'll catch you on the next one.

In Exercises 87–90, find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 55 seconds

Key Concepts

Radian Measure

Angular Velocity

Absolute Value

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