In each case, evaluate z12/(21 + 2). (a) z1 = 10+ j5, 2, = 20/30° Ans. 7.18/27.8° (6) 21 = 5/45°, z2 = 10/-70° (e) z1 = 6-j2, 2g = 1+ j8 Ans. 5.52/23.81° 5.5/15.2° (d) z, = 20, z = j40 17.9/26.6° %3D

Q: 2.3 Find the general solution of p fanx+q tany =lanz

A: Given:   P tanx+q tan y=tanz→           1   is of the form pP+qQ=z:

Q: The approximation of 1 = cos (x² + 3) dx using simple Simpson's rule is: -1.57923 -0.93669 This…

A: The given integral is I=∫01cosx2+3dx To approximate the integral using Simpson's rule.

Q: -3t 10. s = cj e" + c2 e" cos 51 + cz e" sin 51 + 123 O Sm + 5 Su + 17 s - 123 s = 100 O Sm + 17 Su…

A:

Q: In right AXYZ with hypotenuse XZ if cos X = and XZ 10 24. then to %3D the nearest integer XY = ?

A: Given: ∆xyz is the right angle triangle with hypotenuse xz x=710 & xz=24

Q: Use a linear approximation of f(x)=cos(x) at x=5π6 to approximate cos(149∘). Give your answer…

A: Here we have to use linear approximation formula.

Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: If sin u  = 3/ 5 and sin v = 4/5  and that u and v  are  between  0 and π/2,   evaluate :     cos (…

A: given: sinu=35 sinv=45 and u and v are between 0 and π2. we have to evaluate cos(u-v)

Q: 82. Show that cos at cos bt %3D In

A:

Q: 9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 +…

A:

Q: 3. Solve the following IBVP: Ut = Uzz + sin(37x), 00, u(0, t) = u(1, t) = 0, t> 0, u(x, 0) =…

A: Solution

Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

A:

Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

A:

Q: 6) Find (cor dy of

A:

Q: Find L {(2- t) (5 cos 3t 1)}. - 5(s²+9) (s² –9)² 10s - 82-9 5(s2-9) 10s - - s2 s2+9 (s²+9)² 10 82…

A: As we know from the Laplace transformation; 1). La·ft+b·gt=a·Lft+b·Lgt 2). Ltnft=-1ndndsnLft And…

Q: 1. If z = sin2+In^, find the value of x- +y X

A:

Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

A:

Q: If e 17/2- 2i =sin2 then z = %3D - 2i In(sin2) + 4kn -2 In(sin2) + 4kT - 2i In(sin2) – 4kn 2i…

A: Concept : eiθ =cos(θ)+i sin(θ)                  if θ=2kπ                    ei2kπ =cos(2kπ)+i…

Q: Use the Intermediate Value Theorem to show that the equation () 2021 E) - cos(t) = 0 as at least one…

A:

Q: - IF z = tan2 -1 y Show that x- ây

A:

Q: For large-k sin(h) 20k = 2 cos(h) – (9.302) 4h k3 and this gives for (Ao, A1, A2) the values sin(h)…

A: we have the equation  2σk=2cos(h)-sin(h)4h1k2+O1k3 when we divide this equation throughout by 2, we…

Q: e in Q2, find Sin (2e) with 6 If csce -6,

A:

Q: Compute : exp(i sin(e-i))

A:

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

A:

Q: Solve 3 tan(z) = V3 over the interval [0, 27)

A:

Q: Taking Joint H. Ź Fx=0 FHo Cos 45- Fan Cos67.5 Ho +130-6 563 cOszas:0 67.5 45° :: FHo Cos 45-Fan…

A: A system of equation is a set of equation with common variables in them. The solution of such an…

Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

A:

Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: y cos?£ 1-CUSE tanzz

A:

Q: Compute e4 cos (r – 3) dr with two decimal places. Number

A:

Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

A:

Q: 3) z = sin(ej³) + sinh(5230°)

A: We have evaluate the given complex number z=sinej3+sinh5∠30°

Q: Solve the nonhomogeneous opdr – 2rdo = q' In odo. equation

A:

Q: If sin u = 3/ 5 and sin v = 4/5 and that u and v  are  between  0 and π/2,               evaluate:…

A: Given: sinu = 35 ,  sinv = 45  u and v are between  0 and  π2  To evaluate: sin(u-v)

Q: 4 Giren tan A =– where 0<AS Find 2sin 2A.

A:

Q: Ti Ti to 8 Integrate cosh(4z) dz, C any path from - 8 Use the first method, if it applies, or use…

A: Using:- sinhx = -isin(ix)               Sin(-x)=-sinx               Sin (pi/2)=1

Q: Find L {(2 – t) (5 cos 3t – 1)}. 1 g3 10 + s2 +9 - - s2 s(s²+9) O 1 s3 10 + s2 -9 2 - - 8(s2 –9)…

A:

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A:

Q: For cos2(xy) = - evalu COS 4

A: Given

Q: Fand ar a of functrons COSX n

A:

Q: 9 If f(0) = cos 01 ·cos 02·cos 03 ....cos 0n %3D Show, {tan 0 + tan 02 + tan 03 + ... + tan 0,}=- f…

A: First note the results derivative of log x is 1x and derivative of cos(x) is -sin(x). The proof of…

Q: e). Prove that Sin3A+sinA 25in2A -COSA

A:

Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

A:

Q: Use Newton's method with initial approximation x, = 1 to find x,, the second approximation to the…

A:

Q: 9 If f(0) = cos 0 c • cos 02· cos 03. ... cos On f'(0) Show, {tan 01 + tan 02 + tan 03 + ....+ tan…

A: We have fθ=cosθ1·cosθ2·cosθ3....cosθn                 ....(1) Now, we have a formula…

Q: 8. [Calculator Active] Find the least integer value n, such that T,(x)=1-+-++(-1)" - successfully…

A:

Q: If we let u = 4x – 1 for theS 2 tan(4x-1)-3 cos² (4x-1) dx, what will be the resulting integrand?…

A: Solving the problem by finding the integrand.

Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

A: