Question

In the figure, the center of the circle is the origin and its radius is 1 unit. The points A,B are on the circle with ∠AOP = 30°, ∠AOB = 15°.

a. Find the coordinates of A and B.

b. Find the relation between the slope of the lines OA, OB and the tan measures of angles they make with the x-axis.

Answer 1

∆PQR, 30°, 60°, 90° Since OA = 1 then

AQ = \(\frac{1}{2},\) OQ = \(\frac{\sqrt{3}}{2}\)

∴ A\((\frac{\sqrt{3}}{2},\frac{1}{2})\)

∆OBR, 45°, 45°, 90°; OB = 1

OR = \(\frac{1}{\sqrt{2}},\) BR = \(\frac{1}{\sqrt{2}},\)

Slopes of the lines and die tangent valuesof the angles made by the lines with the axis are equal.