Please mention what is v.. based on information provided by you I am able to solve only a) and b)
22 Suppose sin v = 3. Evaluate (a) cos u (c) tan u (b) sin u (d) cos v (e) tan v.
Please solve this question
The image of the parametrization Ф(u, u)-(a . sin(u) . cos(v), b . sin(u) . sin(v), c . cos(u)) with óくa, 0 < u < π, 0 < v < 2π parametrizes an ellipsoid. a) Show that all the points in the image of Ф satisfy the Cartesian equation of an ellipsoid E 2 b) Show that the image surface is regular at all points c) Write out the integral for its surface area A(E), (Do...
cot B-tAn a cos a sin B Sm (50) sin (ae) E Sin (tan u-tan v)
7. You are given that u is an angle in quadrant III with sin u -, and that w is an angle in the first quadrant with tan w = ? . Calculate the exact value of each one of the following: (You should show how you get your answer) (a) cos u (b) tanu (c) sin w (d) cos w (e) sin (u - w) (f) cos (W + u)
(5) The image of the parametrization Φ(u, u) = (a . sin(u) . cos(u), b . sin(u) . sin(e), c . cos(u)) sin(u sin() cosu with b < a, 0 r, 0 2π parametrizes an ellipsoid. u u a) Show that all the points in the image of Φ satisfy the Cartesian equation of an ellipsoid E b) Show that the image surface is regular at all points. c Write out the integral for its surface area A(E). (Do not...
Suppose u and v are in the interval (0, 2), with tanu 2 and tan v = 3. In Exercises 31-40, find exact expressions for the indicated quantities. 36 sin v 40 sec 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...
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)
16, Let x: U R2-, R, where x(8, φ) (sin θ cos φ, sin θ sin φ, cos θ), be a parametrization of the unit sphere S2. Let and show that a new parametrization of the coordinate neighborhood x(U) = V can be given by y(u, (sech u cos e, sech u sin e, tanh u Prove that in the parametrization y the coefficients of the first fundamental form are Thus, y-1: V : S2 → R2 is a conformal...
an 12. Find the exact value of sin(u + v) given that si (Both u and y are in Quadrant II.) Quad Quad sint sin w tsinv= 2 sin sin ut sin = asin (u tv) cos (esty sint cas tant Sinu. as tan sin- sh CUS cas + tan + Cos V = - 12/25 tant Quad I loved it