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

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

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Full solution

Q. Rotate the yellow dot to a location of π2 \frac{\pi}{2} radians. After you rotate the angle, determine the value of sin⁡π2 \sin \frac{\pi}{2} , to the nearest hundredth.
  1. Unit Circle Explanation: Understand the unit circle and the sine function.\newlineThe sine function gives the yy-coordinate of a point on the unit circle at a given angle from the positive xx-axis. The unit circle is a circle with a radius of 11 centered at the origin (0,0)(0,0) of the coordinate plane.
  2. Rotate to (π)/(2)(\pi)/(2) Radians: Rotate the yellow dot to an angle of (π)/(2)(\pi)/(2) radians.\newlineRotating a point to (π)/(2)(\pi)/(2) radians places it at the top of the unit circle, where the coordinates are (0,1)(0,1).
  3. Calculate sin⁡(π2)\sin\left(\frac{\pi}{2}\right): Determine the value of sin⁡(π2)\sin\left(\frac{\pi}{2}\right).\newlineSince the sine of an angle is the y-coordinate of the corresponding point on the unit circle, sin⁡(π2)\sin\left(\frac{\pi}{2}\right) is equal to the y-coordinate of the point at π2\frac{\pi}{2} radians, which is 11.
  4. Round to Nearest Hundredth: Round the value to the nearest hundredth.\newlineThe value of sin⁡(π2)\sin\left(\frac{\pi}{2}\right) is exactly 11, which to the nearest hundredth is still 1.001.00.

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