One of Einsteins most amazing predictions was that light traveling from distant stars would bend around the sun on the way to earth. His calculations involved solving for φ in the equation sin(φ) + b(1 + cos2(φ) + cos(φ)) = 0

(A) Using derivatives and the linear approximation, estimate the values of sin(φ) and cos(φ) when φ ≈ 0.

(B) Approximate the above equation by substituting the approximations for sin and cos.

(C) Solve for φ approximately.