
cos θ cos φ sin φ sin θ, (Beats) Using the trigonometric identities cos(θ verify that φ) (β a) 2 (19) cos ot - cos Bt 2 sin A spring-mass system has an attached mass of 4 g, a spring constant of 16 g/s* and a negligible friction. It is subject to a force of 4 cos(2.2t) down- ward, and is initially 0 at rest. Determine the subsequent motion. Using (19) from Exercise 11, rewrite the solution as the product...
d) Find the area between the two curves (the shaded region). 2 + (2 r=2+cos 2θ ra sin 2θ
d) Find the area between the two curves (the shaded region). 2 + (2 r=2+cos 2θ ra sin 2θ
7) The graph of r = Sin 2θ is given in both rectangular and polar coordinates. Identify the points in (B) corresponding to the points A-I in (A), with corresponding intervals.8) Describe the graph of: r = a Cos θ + b Sin θ 9) Write the equation, in polar coordinate, of a line with (2, π/9) 5 the closest point to the origin.
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...
g and h
g. sin+1-0 sin 2θ-3 cos 26(to find the solutions in [0,2π), use a calc. for this one only) i, sin 2e-V3 cos θ 0
(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...
convert to radians
5) γ 4cos (2θ-5) r 3 (sin(e - 2))2 + 4 cos(20-5) r-6(sin(9-2))2 + 4 cos(2e-5) 9(sin(9-2))2 + 4 cos(2e-5) r 12(sin(e - 2))2 +4 cos(20 5)
5) γ 4cos (2θ-5) r 3 (sin(e - 2))2 + 4 cos(20-5) r-6(sin(9-2))2 + 4 cos(2e-5) 9(sin(9-2))2 + 4 cos(2e-5) r 12(sin(e - 2))2 +4 cos(20 5)
Rewrite-2 sin(x) + 1 cos (z) as A sin (z + φ) Preview A- Preview Note: φ should be in the interval-π < φ < π
. cos? 30 5_4 cos 2θ valuate 0
. cos? 30 5_4 cos 2θ valuate 0
Solve the equation in the interval [0°, 360°). 4 sin^2θ = 3 csc θ = 1 + cot θ 3 sin^2θ - sin θ - 4 = 0 2 cos^3θ = cos θ