Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0^(@)

Question

Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point,  0^(@) <= theta < 360^(@).  P=((2)/(5),-(sqrt21)/(5)) Answer:

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Identify Coordinates: Identify the coordinates of the point P on the unit circle. P = ((2)/(5), -(sqrt21)/(5)) The x-coordinate is (2/5) and the y-coordinate is -(sqrt21)/5.Determine Reference Angle: Determine the reference angle using the arctangent function. The reference angle theta' can be found using the arctangent of the absolute values of the y-coordinate over the x-coordinate. theta' = arctan(|-(sqrt21)/5| / |2/5|) theta' = arctan((sqrt21)/2)Calculate Reference Angle: Calculate the reference angle in degrees. theta' = arctan((sqrt21)/2) Use a calculator to find the value of theta' in degrees. theta' ≈ arctan(2.2913) theta' ≈ 66.4 degreesDetermine Actual Angle: Determine the actual angle theta based on the quadrant where the point P lies. Since the x-coordinate is positive and the y-coordinate is negative, point P lies in the fourth quadrant. In the fourth quadrant, the actual angle theta is given by 360 degrees minus the reference angle. theta = 360 degrees - theta' theta = 360 degrees - 66.4 degreesCalculate Final Value: Calculate the final value of theta. theta = 360 degrees - 66.4 degrees theta = 293.6 degrees

Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0^{\circ} \leq \theta<360^{\circ} . $\newline$ $P=\left(\frac{2}{5},-\frac{\sqrt{21}}{5}\right)$ $\newline$ Answer:

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Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0^{\circ} \leq \theta<360^{\circ} . $\newline$ $P=\left(\frac{2}{5},-\frac{\sqrt{21}}{5}\right)$ $\newline$ Answer: