Search

22 Aug 2023: 3, 2). 10. Basic identities. Starting from the identity sin(A B) = sin A cos B cos A sin B, use the basic properties of the trigono-metric functions (such as ... i) sin(A B) = sin A cos B cos A sin B ;. (ii) cos(A B) = cos A cos B sin A sin B ;. (iii) tan

30 Aug 2019: cos a = cos b cos c sin b sin c cos A. ... sin a cos B = cos b sin c sin b cos c cos A.

17 Jun 2019: π2. 8=. n=1. 1(2n 1)2. [17]. 3B Consider the matrix. A =(. cos θ sin θsin θ cos θ. ). (a) Determine the eigenvalues of A. ... r = (a cos φ sin θ, b sin φ sin θ, c cos θ).

31 Jul 2023: y1(t) = A cos t , y0(t) = B sin t C sin 3t (18). ... for suitable values of the constants A, B and C [recall that cos3 θ = 34 cos θ 14 cos 3θ, and.

4 Aug 2022: Consider the vectors a = (0, 0, 1),b = (sin β, 0, cos β),a′ = (1, 0, 0),b′ =(sin β′, 0, cos β′). ... Show that. |E(a,b) E(a,b′)| |E(a′,b) E(a′,b′)| = |cos β cos β′| 2c0c1|sin β sin β′|.

17 Jun 2019: 1]. (b). J = π/2. 0. sin x cos x dx. ... 4]. (d) The surface S of an ellipsoid is defined parametrically byx = (b sin θ cos φ, b sin θ sin φ, a cos θ), where 0 6 θ 6 π

17 Jun 2019: cos α =(a b) (a c)|a b||a c|. Using identities (1) and (2), prove that. ... cos δ(B, C) = cos δ(A, B) cos δ(A, C) sin δ(A, B) sin δ(A, C) cos α.

17 Jun 2019: b)dy. dxsin x y cos x = 12 sin 2x [5]. ... 2yx=y. (2x2 y)dxdy. Evaluate the integral. [10]. (b) The equation r = (1 cos θ) defines a closed surface in three dimensions.

30 Aug 2019: 6|1〉B, sin. π. 6|0〉B cos. π. 6|1〉B. ). ,(. sinπ. 6|0〉B cos. ... π. 6|1〉B, cos. π. 6|0〉B sin. π. 6|1〉B. ). determine the condition, which α and β must satisfy in order for the measurementstatistics to violate the

17 Jun 2019: 2]. 3 Differentiate(a) ln(x3);. [1]. (b) x cos(2x). [1]. 4 Integrate. ... a) y = (ln x)2 for 0 < x < ;. [1]. (b) y = sin(x) cos(x) for π 6 x 6 π.