calculus questions…


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). 

the figure indicated in the above description.

the exact coordinates of A, B, and C, and label them on your sketch.

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

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

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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