Question

draw the terminal side of an angle in standard position that measures 315°. hint: first plot a point at the origin, then plot a second point anywhere on the terminal side. a. name a point on the terminal side of the angle. b. find the distance from the origin to that point. answer exactly. c. name another angle that is coterminal with the angle you have drawn. question help: video ebook message instructor

Explanation:

Step1: Determine a point on the terminal side

An angle of \(315^{\circ}\) is in the fourth - quadrant. The reference angle \(\theta'=360^{\circ}-315^{\circ} = 45^{\circ}\). For a \(45 - 45-90\) triangle (in the fourth - quadrant where \(x>0\) and \(y < 0\)), if we assume the length of the sides of the right - triangle (formed by the terminal side, the \(x\) - axis, and a perpendicular to the \(x\) - axis) to be \(1\) (for simplicity), a point on the terminal side can be \((1,-1)\).

Step2: Calculate the distance from the origin to the point

Use the distance formula \(r=\sqrt{x^{2}+y^{2}}\). Given \(x = 1\) and \(y=-1\), then \(r=\sqrt{1^{2}+(-1)^{2}}=\sqrt{1 + 1}=\sqrt{2}\).

Step3: Find a coterminal angle

Coterminal angles are of the form \(\alpha=\beta+360^{\circ}n\), where \(n\in\mathbb{Z}\). Let \(n=-1\), then \(\alpha=315^{\circ}-360^{\circ}=-45^{\circ}\).

Answer:

a. \((1,-1)\)
b. \(r = \sqrt{2}\)
c. \(-45^{\circ}\)