Consider the angle shown below that has a radian measure of...

Consider the angle shown below that has a radian measure of 2.7. A circle with a radius of 3 cm is centered at the angle's vertex, and the terminal point is shown. 2.7 rad 3 cm a. What is the terminal point's distance to the right of the center of the circle measured in radius lengths? radii Preview b. What is the terminal point's distance to the right of the center of the circle measured in cm? cm Preview c. What is the terminal point's distance above the center of the circle measured in radius lengths? radii Preview d. What is the terminal point's distance above the center of the circle measured in cm? cm Preview

Transcript

00:01 Okay, so i'm solving this problem involving a circle of a radius of 3 cm.

00:10 And the terminal angle on the circle is at 2 .7 radian.

00:16 Okay, so this is 2 .7 radian.

00:20 And we're finding x and y in both radian and a centimeter.

00:23 So first, to find x, which is the distance from the terminal point to the right of the center of the circle.

00:32 Okay so to find x in radian first you must realize that 3 centimeter is one radius length which is 1 radiant okay so so what we have here is that this is a right triangle and the angle inside you can call that theta or whatever you know, the angle.

01:11 So, data is equal to 180, which is pi in radiance minus 2 .7.

01:23 Okay, so that's how you find data.

01:26 All right, so to find x, you can use the sokatoa trick functions.

01:35 So cosine of data equals x.

01:40 3 centimeter, which is x over 1 radian, because 3 centimeter is one radiance length, so x over 1.

01:49 Basically, so cosine theta equals x, okay? and cosine theta is the same thing as cosine of pi minus 2 .7.

02:05 So using the fact that the cosine ratio is symmetrical, the cosine is symmetrical through the y -axis since if you have cosine of something that is reflected through the y -axis, an angle that's reflected, it's the same is the negative of the positive cosine.

02:34 So if theta 1 was here, then cosine of theta 1 equals the opposite of the the 1 equals the opposite of of cosine of theta since they're on opposite size of the y -axis so they're reflected like that okay so cosine of theta is cosine of pi minus 2 .7 which is the same thing as negative of cosine of 2 .7 okay okay so that so if you put that in your calculator make sure you're on radiant mode you can get the answer for your x in radiance.

03:15 So 2 .7, take the cosine, depends on your calculator.

03:21 Times negative 1 is going to give you 0 .904...

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