Convert the angle 540 ° 540° 540° from degrees to radians .

Everyone, welcome back. So in this practice problem, hopefully, you had a chance to work it out on your own. We're trying to convert this angle 540 degrees from degrees to radians. Let's get started here. How do we do that? We know we're gonna have to use our conversion equations between degrees and radians. I'm gonna either multiply by pi over 180 or the reciprocal, 1 80 over pi. How do I remember which one's which? Well, if I'm trying to go from 540 degrees and I'm gonna end up with something that is radians, forget about the equations for just a second. What I wanna do is I wanna basically cancel out the degrees, and I wanna end up with radians. That tells you which one of these things you're gonna multiply by, because what you're gonna do is you're gonna multiply this by radians on the top, and then you want degrees on the bottom. So in other words, I have to multiply by pi over 180, because you want it basically the degrees to cancel out, and then you're just left with radians on that side. So that's how you can really quickly tell which one you're gonna do. Alright? So it's gonna be pi over 180 times 540 degrees. That's gonna get me radians. Alright. So then I basically can just, I I can cross off a 0 from both of those, and I can just look at these 2 over here. So what is pi times 54 over 18 become? Well, if you have your calculator handy or if you're good at multiplication, you'll actually see that 18 goes into 54 exactly 3 times. So this whole actually, this 54 over 18 just becomes an even number, which is 3. So we have 3 pi radians. Alright? So you might be wondering, why we didn't get a number that's, like, between 0 and 2 pi, and it's just like how we can have angles that are bigger than 360, like 540 degrees or 400 degrees or something like that. We can also end up with radians that are bigger than 2 pi, and that just means that we're going around the circle multiple times. Alright? So, hopefully, you had that right. Let me know if you have any questions. Thanks for watching.

Convert the angle 540 ° 540° 540° from degrees to radians .

3 π 2 \frac{3\pi}{2} 2 3 π rad

5 π 2 \frac{5\pi}{2} 2 5 π rad

0. Functions

Introduction to Trigonometric Functions

Calculus

0. Functions

Introduction to Trigonometric Functions

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Multiple Choice

Convert the angle $540°$ from degrees to radians.

$3\pi$ rad

$\frac{3\pi}{2}$ rad

$\frac{5\pi}{2}$ rad

$4\pi$ rad

Verified step by step guidance

To convert an angle from degrees to radians, use the conversion factor: 1 degree = $ \frac{\pi}{180} $ radians.

Multiply the given angle in degrees by the conversion factor to convert it to radians. For the angle 540°, the calculation is: $ 540 \times \frac{\pi}{180} $.

Simplify the expression by dividing 540 by 180, which results in $ 3 \times \pi $.

The simplified expression gives the angle in radians: $ 3\pi $ radians.

Verify the result by checking the options provided: $ 3\pi $ rad is one of the correct answers.