Suppose an arc of length s lies on the unit circle x² + y² = 1...

Question

Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating at the point (x, y). (See Figure 12, repeated below.) Use a calculator to find the approximate coordinates for (x, y) to four decimal places.
s = ―7.4
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s = ―7.4

Accepted Answer

Welcome back. I am so glad you're here. We're told to consider an arc of length P on the unit circle which is X squared plus Y squared equals one. The starting and terminating points of the arc are +10 and XY respectively. With the help of a calculator determine the approximate coordinates of the point XY. When P equals negative 6.8 round, the answer to four decimal places, then we have a figure, we have a vertical Y axis, a horizontal X axis. They come together at the origin in the middle overlaying. On that figure, we have a unit circle and every X and Y intercept for our unit circle is exactly one unit away from the origin. And then we also have an angle on top of our unit circle. The initial side of our angle is through the positive part of the X axis. And the terminal side is in the fourth quadrant and where that terminal side intercepts with our unit circle. That's where our point XY is located. So those are the coordinates we're trying to find. Then there's a little bit more information on here. We're reminded that our arc is of length P and we're told that X equals the cosine of P and that Y equals the sign of P. Our answer choices are answer choice. A negative 0.4941 0.8694. Answer choice B negative 0.86940 0.4941. Answer choice C 0.86940 0.4941. And answer choice D 0.8694 negative 0.4941. All right. So we recall from previous lessons that when we have an arc length of P that our X value on the unit circle is going to be equal to the cosine of P and the Y value will be equal to the sine of P. So this is just a matter of plugging in, in our calculator first, you want to make sure that you are in radiance mode, you'll have the cosine of our P value is negative 6.8. And you will get approximately when you're rounding 24 decimal places, 0.8694. And then for the sign of negative 6.8 you'll get approximately when you're rounding to four decimal places, a negative 0.4941. And this makes sense, we have something in the fourth quadrant. So our X value is positive and our Y value is negative. So if we write that as an ordered pair. That's 0.86. Oops, not comma 0.8694. Comma negative 0.4941. And we look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating at the point (x, y). (See Figure 12, repeated below.) Use a calculator to find the approximate coordinates for (x, y) to four decimal places.
s = ―7.4
<IMAGE>

Key Concepts

Unit Circle

Arc Length

Radians and Degrees

Watch next

Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating at the point (x, y). (See Figure 12, repeated below.) Use a calculator to find the approximate coordinates for (x, y) to four decimal places. s = ―7.4 <IMAGE>

Key Concepts

Unit Circle

Arc Length

Radians and Degrees

Watch next

Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating at the point (x, y). (See Figure 12, repeated below.) Use a calculator to find the approximate coordinates for (x, y) to four decimal places.
s = ―7.4
<IMAGE>