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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