Calculus question....

timer Asked: Dec 6th, 2014

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 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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