6te" Sin " Cos 7t 10.) f( t) = 2 2

Q: 3. f(t) = 2e3t sin 2t – 3e3t cos 2t -

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Q: sin (t) -dt 3 (4+ cos (t))?

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Q: 4 TT 37. tanα < a < T; cos B = 2' 50 < B < -- %3D 3 2 2

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Q: 2cos'z = COS T Select all correct solutions.

A: Follow the procedure given below.

Q: The appropriate trigonometric substitution for * dx is V3x-x 3 3 X ==+ sin 0 2 2 sec 0 4 2 O Option…

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Q: | 12sin z cos zý3 sin? z + e® dz

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Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: Find A°, where (cos(7/5) -sin(T/5)) A = sin(T/5) cos(T/5)

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Q: Q4:B/Simplify Moivre's theorem? [cos 30+ i sin30 15 [cos 0-i sine 1³ [cos 50+ i sin50 ] [cos 20-i…

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Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: V125 cos - j sin 11 11 1. Simplify . Express answer in rectangular form. 47 + j sin J5 cos 11 11

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Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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Q: Q2/provethate Cos17 +SinI7 cos17-Sın17 %3Dtun62

A: We have to prove that                               cos17°+sin17°cos17°-sin17°=tan62°

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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Q: 9. Decide whether or not the following equations are true or false: e° = cos" r + sin² r = cosh? r –…

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Q: r=2 Sin cQ-Ę) Cos co-Ę)

A: The given equation is r=2sinθ-π4cosθ-π4 Apply the formula sin2θ=2sinθcosθ to get:…

Q: 3. Express the following function in terms of 'Sine & Cosine'; y (t) = 4 sin 2nt + 15 cos 2nt [

A: please see the next step for solution

Q: Find 7'(t), given 7(t) - 4e 2t (3 sin(2t), ,4 cos(4t)). F'(t) =

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Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

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Q: 3. x = cos³ 0, y = sin 0 4

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Q: Find LT of (i) e(2 cos 5t – 3 sin 5t) 3t (ii) e²ª cos? t (iii) e* sin 2t cos t

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Q: 1/2 sin 12 y cos' y dy y

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Q: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: Q9: If F(x, y, 2) = [sinh-(sin- (In (/sin(cos(x²)) y? + zyx + y, find and ду az Q10: If z =…

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Q: Hw/ plot O r=2.2 Cose O r: 5+3 Cos e Or=l+2 Cose Or: 2. Cos O r=S-Sin 8 between 8=0 4

A: (1).  The given polar curve is: r=2+2 cos θ

Q: Z is a complex variable z=x+iy  question attached as photo

A: Consider the closed integral

Q: f(t) = 5e-3t – 3 cos 3t + 6 sin 5t – 9. %3D

A:

Q: r = 17 sin 2t i - 17 cos 2t j

A: Given equation r= 17 sin 2t i- 17 cos 2t  j

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: 2. Find sin(72) -dz. where C: z(t) = 2 cost+i (2 sint). Os ts 2m.

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Q: Zcos?x+Sinx-|-0 COS Solve for 0L X Y

A: To find the value of x

Q: V 3 (d) r(1/6 + At) - r(n/6) = 3 COS At sin At cos At + SV3 sin At it

A:

Q: "+2y + 5y = 6 sin 2r +7 cos 2r

A: Given that y''+2y'+5y=6sin2x+7cos2x The objective is to solve the equation, Now let's consider…

Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: (2{co(;)+ sin(;)})" Simpli fy, z = 1+v3i 0 22품 0 22플 O 42 O 24-

A: We have to simplify

Q: • Cos C = BE AC Cos 30°: y %3D 6.Cos 30', l603_ - 303 a %3D r 5.3 y: 313 5.2 yo

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Q: b. sin? () = 2 over [0, 2n) %3D

A: EXPLANATION

Q: The appropriate trigonometric substitution for dx is V3x-x2 ww 3 X = 9 3 + sec 0 2 4 3 +sine x = O…

A: We have to solve

Q: T/4 sin2 x 2. :- cos? dx CoS2 COS x 7/4

A: To find the value of the given integral.

Q: The value of 6 Jo° (4+ cos2x)dx is: 글(똥-0.5) 1 ( 47 4T 글(똥 +0.5) 3 None 글(품 + 0.5) 1 4 3

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Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: 0. sin*(x) dx = R, 3 -Tt, what is 8. Given that sin (0) de?

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Q: (4x-) What is Y*? 2 Let Y = cos ( 4X

A: Step 1: Consider the given function:

Q: (a) y" + 3y' – 2y = -e2" (5 cos 2r + 9 sin 2a)

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Q: Q: Evaluate : fe 1- cos 2ax dx. 1+ sin 2 ax 2ax

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Q: Given, w=2iz - sin iz. Find i dz 2+ cos iz -2- cos iz -2+cos iz -2+cos z

A: image is attached

Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

A: