Questions: Determine the point (x, y) on the unit circle associated with the following real number s. Write the exact answer as an ordered pair. Do not round. s=135°

Solution Steps

To determine the point \((x, y)\) on the unit circle associated with the angle \(135^\circ\), we need to convert the angle from degrees to radians and then use the unit circle properties to find the coordinates. The unit circle has a radius of 1, and the coordinates \((x, y)\) can be found using the cosine and sine of the angle in radians.

To find the coordinates on the unit circle for the angle \(135^\circ\), we first convert the angle from degrees to radians using the formula: \[ \text{radians} = \frac{\pi}{180} \times \text{degrees} \] \[ \text{radians} = \frac{\pi}{180} \times 135 = \frac{3\pi}{4} \]

Using the unit circle properties, the coordinates \((x, y)\) can be found using the cosine and sine of the angle in radians: \[ x = \cos\left(\frac{3\pi}{4}\right) \] \[ y = \sin\left(\frac{3\pi}{4}\right) \]

For \(\theta = \frac{3\pi}{4}\): \[ \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2} \] \[ \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} \]

Final Answer