https://www.desmos.com/calculator/2fnugmbwte X a) The blue shaded region A, of the unit circle is a sector with central d) The vertex of the triangle corresponding with B is B(x, h). Use the angle y. The tan shaded region A, is a right triangle with base fact that B lies on the unit circle centered at the origin to write measuring x and acute angles a, B. The elementary geometric area formulas give h = h(x) = e) With the above we are able to write the shaded areas as functions A1 = = and A2 = of X: b) Since B, y are [ CIRCLE ONE: vertical / alternate / corresponding ] A, = A (x) = angles, we conclude that and B = A2 = A,(x) = c) We know that f) Write the sum of A, and A, as a single definite integral sin B = b(x) f(t) dt. so that we can write Y = Y ( x) = _ A + A2 =