In the triangle pictured, let A, B, C be the angles at the three vertices, and let a, b,c be the sides opposite those angles.

According to the ``law of sines,'' you always have:
b/a=sinB/sinA

Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is ?/4 radians=45o and the angle B is ?/3 radians = 60o. You then widen A to 46o, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B.
(a) Notice that the angle B is a function of the angle A; i. e. B=f(A). Consequently, it makes sense to calculate the implicit derivative:
dB/dA
=(?3) / (?2)=
(b) Calculate
dB/dA
when A=?/4 and B=?/3; leave your answer in EXACT FORM:
(c) Write the linear approximation of f at A= ?/4:
(A ?/4) +
(d) Using (c), when A= 46o, B is approximately
degrees; either answer exactly or to three decimal places.