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2. [15 points]Simplify the following expression Jw 3 C) cos(π) )-(2, +3) (b sin kw S(w)
(b) (2 pts) (t) is given as r(t) e sin(t) Find X(jw). Show that X(jw) = 25 + (w- 1)225(w+1)2 (c) (4 pts) x(t) is given as x(t)-π inc(t) cos(nt). Find X(jw) (d) (4 pts) 2(t) is given as 2(t) e Áil+ 3) + e' ỗ(t-3). Find X (jw). Simplify the answer as (e) (4 pts) 2(t) is given as r(t) = rect(2(t )) reetgehj)). Hint: use Fourier Transform pair: sine(t)艹rect( ) much as possible Find X(jw). Simplify the answer...
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e Define f: R2R3 b f(s,t) (sin(s) cos(t),...
(1 point) Simplify each expression. sin(x) + sin(-2) = sin(20) sin(-x) + cos(-2) cos(x) cos(x) + cos(-x) = Note: You can earn partial credit on this problem. Entered Answer Preview
5. Simplify the following expression: tan(@)sin (20) 2 + cos (0) sec (-0)
Simplify the following trigonometric expression by following the indicated direction sin 0 1 + cos 0 Multiply 7- cos o by 1 + cos 0 sin e 1 + cos 0 1 - cos ' 1+ cos = *cos (Simplify your answer.)
9. [-12.94 Points) DETAILS SPRECALC7 7.1.017. Simplify the trigonometric expression. cos(x) + sin?(x) cos(x) 10. [-12.94 Points] DETAILS SPRECALC7 7.3.003. Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) ex in Quadrant 1 sin(2x) = cos(2x) = tan(2x) 11. [-12.94 Points] DETAILS SPRECALC77.3.022. Use an appropriate Half-Angle Formula to find the exact value of the expression. sin(105)
Supposez1 =4 cos 3 +isin 3 andz2 =2 cos 6 +isin 6 . Computez1z2. (a) 8(cos?π?+isin?π?) 22 (b) 4(cos?4π?+isin?4π?) 66 (c) 2(cos?π?+isin?π?) 66 (d) cos(π)+isin(π) (e) 8(cos?π?+isin?π?) 66 17. Suppose z1 = 4 (cos (1) + i sin (5)) and z2 = 2 (cos () + i sin (7)). Compute z122. (a) 8(cos (7) + i sin (7)) (b) 4(cos (4) + i sin (*)) (c) 2(cos (7) + i sin ()) (d) cos(T) + i sin(TT) (e) 8(cos (7)...
2. LetA = 〈cos-, sin? and B = 〈cosi' sin, be two vectors on the x-y plane. Let -(cos-, sin π〉 3 4 be another non-zero vector on the x-y plane not collinear with A or B. Show that A × B =-B × C. If we could cancel B, as we could if these were real numbers, is it true that A =-C? [Show your work and conclusions on a separate sheet of paper] 2. LetA = 〈cos-, sin?...
Simplify the following trigonometric expression tan(a) sec(0) - cos(e) sin(0) csc() seco) 1 + cos(20)