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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

1 Nov 2023: For b > 0 and x R, we have. cos(x ib) = 12(ei(xib) ei(xib)) = 1. ... 2(ebeix ebeix). and thus Re (cos(x ib)) = cosh(b) cos(x) and Im (cos(x ib)) = sinh(b) sin(x).

9 Oct 2023: F8. (a) i. (b) 1. (c) 12(1 i). (d) e(cos 1 isin 1). ... F13. (a)sin 6θ sin 5θ sinθ. 2(1 cosθ). (b). cos 6θ cos 5θ cosθ 12(1 cosθ).

17 Jan 2023: α, β, and γ all 90º. A reminder cos(0)=1 cos (90)=0 sin(0)=0 sin(90)=1. ... v v = |v| x |v| x cos(0)=x2 y2z2. |v| = (x2 y2z2)1/2.

20 Nov 2023: cos φm = A Be2, (12). and A and B are functions of a/aN that should be determined. ... φ̈ = (A B cos φ) sin φ, (19). where A and B are functions of the orbital parameters of the particle and satellite that should be determined.

9 Nov 2023:  , G =. y cos(xy) by (b c)z. x cos(xy) bx bz(c b)x by. ... a) Find the general solution of the differential equation. d2y. dx2+ y = cos(kx) ,. where k is a positive integer. [10]. (b) (i) Rewrite the set of simultaneous differential equations

26 Mar 2023: cos nθ , (6.6). so that, on r = R2 = b β cos nθ ,pr. ... r=R2. = 6μh3. dhdt. (b β cos nθ ) [n k̂ bn1 n m̂ bn1.

3 Oct 2023: a)d. dx(sin x) (b). d. dθ(cos θ). (c)d. dt(tan t) (d). ... x2 4)dx (b) 20. (xa)2dx. (c) π0eiθdθ (d). π0. cos(x)dx. (e)π/4π/4.

4 Oct 2023: S(t) = cos 2ωtS (1 cos 2ωt) B̂ (B̂ S) sin 2ωt B̂S. ... H = γB(t) S where B(t) = B0ẑ b (x̂ cos ω1t ŷ sin ω1t).

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.