# calculus questions...

**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 30^{O}, 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 30^{O}). 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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