question 17 (1 point)\npage 17 of 35\np(-6,7) lies on the terminal arm of an angle in standard position…

question 17 (1 point)\npage 17 of 35\np(-6,7) lies on the terminal arm of an angle in standard position. what is the value of\nthe principal angle θ to the nearest degree?\n\na) 311°\n\nb) 229°\n\nc) 131°\n\nd) 49°\npage 17 of

question 17 (1 point)\npage 17 of 35\np(-6,7) lies on the terminal arm of an angle in standard position. what is the value of\nthe principal angle θ to the nearest degree?\n\na) 311°\n\nb) 229°\n\nc) 131°\n\nd) 49°\npage 17 of

Answer

Explanation:

Step1: Calculate the reference angle

Given the point (P(-6,7)), we first find the reference angle (\alpha). The formula for the reference angle when (x<0,y>0) (second - quadrant point) is (\alpha=\arctan\left(\frac{|y|}{|x|}\right)). Here, (x = - 6,y = 7), so (\alpha=\arctan\left(\frac{7}{6}\right)). Using a calculator, (\arctan\left(\frac{7}{6}\right)\approx49^{\circ}).

Step2: Find the principal angle

Since the point (P(-6,7)) is in the second - quadrant ((x<0,y>0)), the formula for the principal angle (\theta) in standard position is (\theta = 180^{\circ}-\alpha). Substituting (\alpha\approx49^{\circ}) into the formula, we get (\theta=180^{\circ}-49^{\circ}=131^{\circ}).

Answer:

C. (131^{\circ})