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Rotate the yellow dot to a location of (pi)/(2) radians. After you rotate the angle, determine the value of tan ((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 tan⁡π2 \tan \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 tan⁡π2 \tan \frac{\pi}{2} , to the nearest hundredth.
  1. Understand the unit circle: Understand the unit circle and the tangent function.\newlineThe tangent of an angle in the unit circle is the ratio of the y-coordinate to the x-coordinate of the point on the unit circle at that angle. However, at π2\frac{\pi}{2} radians, the point on the unit circle is directly above the origin, meaning its coordinates are (0,1)(0, 1). This makes the x-coordinate 00.
  2. Calculate tan⁡(π2)\tan\left(\frac{\pi}{2}\right): Calculate the value of tan⁡(π2)\tan\left(\frac{\pi}{2}\right).\newlineSince tan⁡(θ)=sin⁡(θ)cos⁡(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} and at θ=π2\theta = \frac{\pi}{2}, sin⁡(π2)=1\sin\left(\frac{\pi}{2}\right) = 1 and cos⁡(π2)=0\cos\left(\frac{\pi}{2}\right) = 0, we have tan⁡(π2)=10\tan\left(\frac{\pi}{2}\right) = \frac{1}{0}. This is undefined because division by zero is not possible in mathematics.
  3. Conclude tan⁡(π2)\tan\left(\frac{\pi}{2}\right): Conclude the value of tan⁡(π2)\tan\left(\frac{\pi}{2}\right).\newlineSince tan⁡(π2)\tan\left(\frac{\pi}{2}\right) is undefined, we cannot provide a numerical value to the nearest hundredth or any other precision.

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