sen(2u) if we know that cos(u)=8/ square root 64+25x^2 sin(2u) if cos(u)=8/ square root 64+25x^2 Sen...
Sin
and Cos
V15 13. Si sen(a) y está en el cuadrante III entonces sen 10 10 I. B. C.- 4 D. 4 4 14. cos(10")cos(59) + sen(10°)sen (5) = A) sen(5) B) cos(15) C) -cos(5) D) cos(59) 15. _1 + cot-(t) - csc (t) = A) 1 B) 4 C) 0 D) -1 16. 3 sen(x) + 2 sen(x + 2) = A) 5 sen(x) B) -5 sen(x) C) 5 sen(x) + 1 D) 5 sen(x) + 2
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...
If we know the values of sin(x) and cos(x), we can find the value of sin(2x) by using th rmula for Sine. ---Select-- Half-Angle Double-Angle State the formula: sin(2x)
8. Let w cos(2π/5) + isin(2π/5). Here we describe how to express w in terms of square roots. (a) Show that w is a root of the polynomial 24+2+22+21. Hint: 25-1-(-(24+23+22+2+1) (b) Show that w + is a root of the polynomial u2 + u-1 (c) Show that Ve, where V5 means the positive square root of Hint: Figure out the sign of w by adding the polar forms of w and 1/w. (d) Put β--12vS So in part (c),...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
7.6 #19 ES root of y=5=2-root y-4 the index is 2 so I square both sides of the equation. I got as far as (5)^2=-4 root y-4. the answer in the book is 25+64=16y-64+64 (I would like to know how did 64 come about and how did they get 16y?
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...
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)
2^x-8/8=square root of 2
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.