# Calculus question....

**Question description**

1. Consider the following situation: A circle of with center *O(0,0)*, radius 10m, is inscribed in a square. The ray of angle 30O, in standard position, intersects the circle at point *B*, and continues to intersect the square at point *C*. Let A denote *(10,0). *

(i) Sketch the figure indicated in the above description.

(ii) Find the exact coordinates of *A, B*, and *C*, and label them on your sketch.

(iii) Now suppose we have arbitrary acute angle Q (in radians, instead of the 30O). Again draw the sketch!

(iv) Again figure out the exact coordinates of *A, B*, and *C *and label them on your sketch. NB: You will use trig functions here!

(v) Now figure out the equation you would have to solve to find Q to make the area of *ABCA *exactly equal to the area of the sector. HINT: This means area of sector is half area of triangle. (You cannot solve such an equation exactly – this is an example of a TRANSCENDENTAL equation, so the theorems of algebra do not apply.)

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