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Rotate the yellow dot to a location of (3pi)/(2) radians. After you rotate the angle, determine the value of cos ((3pi)/(2)), to the nearest hundredth.

Rotate the yellow dot to a location of 3π2 \frac{3 \pi}{2} radians. After you rotate the angle, determine the value of cos⁡3π2 \cos \frac{3 \pi}{2} , to the nearest hundredth.

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Full solution

Q. Rotate the yellow dot to a location of 3π2 \frac{3 \pi}{2} radians. After you rotate the angle, determine the value of cos⁡3π2 \cos \frac{3 \pi}{2} , to the nearest hundredth.
  1. Understand unit circle and cosine: Understand the unit circle and the cosine function.\newlineThe cosine of an angle in the unit circle is the xx-coordinate of the point where the terminal side of the angle intersects the unit circle. The angle 3π2\frac{3\pi}{2} radians corresponds to 270270 degrees, which is at the bottom of the unit circle where the xx-coordinate is 00.
  2. Calculate cosine of (3π)/(2)(3\pi)/(2): Calculate the cosine of (3π)/(2)(3\pi)/(2) radians.\newlineSince the angle (3π)/(2)(3\pi)/(2) radians is at the bottom of the unit circle, the x-coordinate at this point is 00. Therefore, cos⁡((3π)/(2))=0\cos((3\pi)/(2)) = 0.
  3. Round to nearest hundredth: Round the result to the nearest hundredth.\newlineThe value of cos⁡(3π2)\cos\left(\frac{3\pi}{2}\right) is 00, which to the nearest hundredth is 0.000.00.

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