MAT 21A Lecture 13: MAT21A Lecture 13

(1 point) Find an arc length parametrization of r(t) -(e' sin t, et cos t, 2e) ri (s) = (

5. (a) We showed in class thate- cos() +isin(). where i is the complex number such that #2-1 (or-v-1). Rederive this equality using power series. (b) Use the identity in (a) to show the identities cos(A+B) co( A) cos(B) -sin(A) sin(B) and sin(A + B) = cos(A) sin(B) + sin(A) cos(B).

Evaluate the work done between point 1 and point 2 for the conservative field F. F = 5 sin 5x cos 6y cos 2zi + 6 cos 5x sin 6y cos 2z j + 2 cos 5x cos 6y sin 2zk ; P1 (0, 0, 0), P2 W = 0 W = -2 W = 2 VV = 1