Prove the trigonometric identity: sin(x + y) sin(x - y) = sin’x – sin? y. Which identity is used to prove it true? sin(x + y) = sin x cos y - cos x sin y All of these. tan o sin e cos e cos? 0 = 1 - sin? 0
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
14. (6 points) Use sin(– ) = sin r cos y – cos sin y to evaluate sin ( - 7). BONUS. (8 points) Find all r values in (0,27 that satisfy the following equation. sin cos? Hint: sin?. + cos2 = 1.
Prove the trigonometric identity: sin(x + y) sin(x - y) = sin’ x – sin? y. Which identity is used to prove it true?
Prove the trigonometric identity: sin(x + y) sin(x - y) = sin² x – sin? y. Which identity is used to prove it true?
5. Prove the following identity. (sin x + cos x) = 1+sin 2x 6. If cos(x) = , and x E QIV , find the exact value of each of the following. a.sin (2x) b.cos cos()
Is the following equation an identity? If so, prove it. sin- x - cos x cos x = sin’x - cos x The given equation is an identity. sinx - cos*x = (sin’x)2 – (cos?x)2 = (sinºx – cos x) (sinºx + cos²x) = (sin x – cos2x) (1) = sinºx - cos x. The given equation is not an identity. The given equation is an identity. sin- x - cos*x = (sin?x)2 – (cos2x)2 (sinºx – cos x) (sinºx...
13. Evaluate, S sin 5x cos x dx. Also prove that, 52" sin mx cos nx dx = 0 Using reduction formula *****
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...
1. Prove that the map defined on generators by sin θ cos θ and extends to give an injective homomorphism of D4 into GL2(R). (Hint: First determine the image of all elements of D4 under then map ф.) 1. Prove that the map defined on generators by sin θ cos θ and extends to give an injective homomorphism of D4 into GL2(R). (Hint: First determine the image of all elements of D4 under then map ф.)