8. Let 2ni S7 = e7 = cos- 27 + isin- 7 7 a. Prove that E¢ = 0 k=0

Q: Let 7(t) = Find dt (don't include the +C)

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Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: 8. where Tt LO L JC COS = 17 find Jan -7-

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Q: Let o,= 2 (cos 45° + i sin 45°), @,= (cos 30° + i sin 30°), calculate a. @j @2= b. o, / 0,= с. О d.…

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Q: in Let z = 0.5 +",., Find e 6z 3 C) e3 F) e-0.5 (cos 2 + isin2) A) -e 20 B) e-5* (cos 20 + isin20)…

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Q: 3. Evaluate by hand the following To (a) (cos nwot, cos mwot)= coS nwot cos mwot dt when m tn То (b)…

A: To calculate the given trigonometric integrals

Q: A periodic signal is given by r(t) = 3 cos(t) + cos (5t 2n - 2 sin (8t + 3

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Q: ( 5) Find f (o) and f (0) f Ga)= .3 if x° Cos (x3)

A: Taylor series expansion

Q: Let 7(t) = VE + 4, cos(t), te-'> (t*), te¯t >

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Q: Use a linear approximation to estimate cos 29° Answer. The approximate value of cos 29° is O cos 29°…

A: Given, cos 29°

Q: 11) (3ysos(3a By cos(3

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Q: 3. Compute : exp(sin m(e÷)).

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Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

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Q: 9. Let r = 3 sin tî + 3 cos tj + 4tk. Calculate N

A: Given r(t) To find N(t)------ unit tangent vector

Q: Which one of the following is L *{Z16 e-3s}? s2+16 Select one: O cos((t – 5))U(t – 5) О os(4(t…

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Q: dy Find ax if y cos (Tx) O 1) sin(x) 2) 3ncos2(Tx)sin(nx) 3) -37cos 2 (TY)sin(Tx)

A: we have to find

Q: 4) Find the value of cos(1.74) from the following table oot x y = sin(x) Hint: dy dx 1.7 0.9916…

A: The given problem is to find the value of cos(1.74) by using newton divided difference method from…

Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: 10. Compute the following: »TT/4 (a) COS dx 3 (b) dax

A: Part (a)-Given:

Q: -24-4s e S COS os(28) – 7 sen(28) cos s+6 s2 + 49

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Q: السؤال 7 1 B (m,n) =2 sin2m – 10 cos2n – 10 de ylgn O İhi O

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Q: If L{cos(ax)} then find L{x³ cos(ax)}. %3D p2+a²

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Q: 11. sin t coS ! cosistin oni 12. (t + 1)8 bis eatlosono 14. 13. gnollot eft 2sob

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Compute L{2et – 3 cos(7t) + t³}. а.

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Q: Consider (e cos 4 + ie sin 4) (11+12:) cos 4+ ie sin 4) (11+12i) 3DZ What is the general value of z?…

A: Euler's formula is given as that e^(ix) = cos(x) + i sin(x).

Q: Solve the following 1 do +- PDE: dr'r dr',2 20? BCs: v, dr at r=a v, =U„ cos 0 at r= 00 1 дф Ve = =…

A: The objective is to find the solution of partial differential equation, ∂2ϕ∂r2+1r∂ϕ∂r+1r2∂2ϕ∂θ2=0…

Q: 1. Compute the following double in- 2. C tegrals. tegr a. STr 2.x + 4y + 10xy dA, R : 0 < x < 1,0 <…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

Q: 9/8 2* CoSメーenp and X=/t+] its dus

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Prove thet (1+ cose -isine)" +(l+ Cos e+isine)" = 2""cos (em). %3D Co."(을) COS

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Q: And periad of :- yatan 4x @ yosco 5 Cos 10X 2) "Q2 S Ske kch these famckan g- these fanction g- L ye…

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Q: if Sn0=4. and cos a=5 evalute witrout 13 using Aables Cos (eta)

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Q: 11 Ifx = Arc cos then x is equal to 1) 120° 2) 150° 3) 210° 4) 300°

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Q: B. Let ulr,e) = r"sin(ne). Find 4 2n-2 +u -nr Ure or

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A: Complex integration of the function

Q: Suppose sin(0) = and 0 < 0<T/2. Compute cos(0). (Hint: SOH-CAH-TOA) V3 3 3

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Q: 2 7 4 is S cos' xsin xdx 비

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Q: 4. Write u = -2 cos Tt – 3 sin at in the form u = Rcos(wot – 8).

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Q: Given that cos(2t) = 2 cos (t) – 1, it follows that L{cos"(t)} =;( +:). O True O False

A: We need to find Laplace Transform of f(t) = cos2(t) But , cos2t = 2cos2(t) - 1  ⇒ 2cos2(t) = 1 +…

Q: 17. If 2 tana tan?ß tan?y + tan a tan-ß + tan B tany + tan?a tan?y 1 (a. B.y e R. a. B.y (2x+1)…

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Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

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Q: 3. Find osse(t), sa(t), Qusa(t) for a message signal given by m(t)-cos 100nt cos200mt. If the…

A: Consider the given message signal, mt=cos100πtcos200πt Using the formula cosAcosB=12cosA+B+cosA-B we…

Q: Which of the following is equal to S ešin ® de ? A. e+ cos e+ C 8. ecos + C Option 1 Option 2 C.…

A: Given:    Intergral of esinθ dθ

Q: if z, = (1 – v31) and zz = (V3 + i) by De Movier's theorem z,z– 4% = 1 (cos( +5 + isin +5)

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Q: 5. Evaluabe the following integrarls s sin thdz 471 ans2 3. Co sh 2 -277 dz ,c: 1 1 ans:

A: Your answer of First integral is not match my answer, either the expression of  integrand is…

Q: Evaluate L{cos (3+2t) } scos3 + 2sin3 A s2+4 scos3 – 2sin3 B s2+4 (s+3)2+4 (s+3) 2–4

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Q: Given that 7(1 + h) – 7(1) = (h - 1 + cos(h), e" -e-", In(2h + 1)) for all h where -. a 7'(1 :…

A: We will use the definition of derivative to find r'(1) as shown below

Q: Find the exact values of sın 20 and cos 20 for cos e on the interval 0° S 8590° sin 20= 0.7744, cos…

A: Use the identity sin2θ+cos2θ=1 to evaluate the value of sin θ. sinθ=1-cos2θ=1-372=1-949=4049=2107

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.