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8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
8. Solve the equation 1-sin = cos on the interval 03 0<21. (12 pts)
19. If the cos u= -5/13 where it <u<37 12 and sin v= 8/15 where tan v<0, find sin (u+v)
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
10. Consider the surface S parameterized by w r= (cos y, sin v, u + sin v), -3 <u <3, 050 < 27 *** (a) Write a linear equation for the tangent plane to the surface at (0,1,1) (b) Compute the surface area of S.
12. (8 points) Solve (sin 0)2 = 5.0 5 0 < 2t.
2. Solve 2 sec @ + tan 0 = 2 cose, 050<21. 3. Solve cos 2x + 3 sin r-2=0, 0 <x<360°.
Solve the following problem อน a( 1,0) = 0, a(2,0) = f(0), 0 < θ <う
Question. Consider () - ( cos(t), sin(t)) for 0 +< 2. Parameterine this curve by are length. Chat
Solve fort, 0 < t < 27. 32 sin(t)cos(t) = 12 sin(t)
Solve the equation on the interval 0 5 0 < 21. 5 sine - cos a = -1 00, 40 , 7 0 37 | O None 00, 2