calculus questions…

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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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