AC = d and %3D INДАВС, АВ In ABCD, CBD = 0,BĈD = B,BC Use the cosine rule to show x = 2d cos 0 В, ВС = x and DC = k %3D %3D %3D 6.1 d sin 20 6.2 Now show that k |3D sin(0 + B)

Q: 27. Inside the circle r = 3a cos 0 and outside the cardioidr = a(1+cos 60), %3D %3D a > 0

A: Find the area of the region inside the circle and outside the cardioid, where the equation of circle…

Q: e*, when 20 = -1 %3D P„(x) sin(nrx) – nn cos(nax), when 2, = (nx)² for n = 1,2,3,.... a.) Show that…

A: Hi! As the questions are lengthy, we are answering only the first subpart. If you need an answer to…

Q: Given f(0) = 7 cos 0 + sin 0. %3D a. Express f(0) in the form of R cos (0 – a) for R > 0 and 0° < a…

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Q: Find the length of the curve. cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< n/4

A: We have to find the length of curve.

Q: Given (x,y) In(2xy) where x(u,v)=e" cos (4v) and y(u, v) = e" sin(4v). Find sin x cos x [Hint: tanx…

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Q: 4. 1+(sin (20))2 6 cos (20)d0 4. 1+ (sin (20))2 6 cos (20)d0 a f(u) du where g(x) =u, to evaluate…

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Q: Find the length of the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

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Q: find area Inside the oval limaçon r = 4 + 2 cos 0 Inside the cardioid r Inside one leaf of the…

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Q: Evaluate the integral. 1/2 | [4 cos 5t i - 4 sin 3t j+ sin? 7t k] dt 1/2 | [4 cos 5t i - 4 sin 3t j+…

A: We have to solve given problem:

Q: If cos t = - and t is in the 3rd quadrant, then sint = %3D V32 6 V40 6 V32 2 V32 6 O V32 2

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Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

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Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

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Q: The cos'ydy is equal to 3 A. siny + sin?y +sin³y - sin'y+ C sin'y + C 3 1 B. siny – sin³y + siny -;…

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Q: Solve the problem Utt = 81uzz; ВС: и(0, t) — и(1, t) — 0 IC: u(x, 0) = 4 sin(2rx), PDE: 0 0 ВС:…

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Q: Let z(x, y) = xy where x = r cos(80) & y = r sin( - 50). %3D | дх ду дх ду & ar' ar' a0 az dz & ar…

A: Let z = f(x,y), then,   ∂z∂r =∂z∂x · ∂x∂r + ∂z∂y · ∂y∂r   ∂z∂θ =∂z∂x · ∂x∂θ + ∂z∂y · ∂y∂θ

Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: Let z x = 2 cos u, and y 3 sin v. Find dz in terms of u and v. %3D Provide your answer below:

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Q: What is the general solution of (r +sin 0 cos 0) dr + r (sin 0 + cos 0) de = 0 ? - rsino rcose = C…

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Q: Use Green's Theorem to evaluate |(3ye2* – 7 sin? (3x* )) dx +(5x* +2x’y² +8e*-1y+2 where C is the…

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Q: Evaluate f sin (3t) cos(3t) dt Select one: a를sin(3t) + C b. sin (3t) + C . 습sin"(3t) + C o 18 d. sin…

A: Given:

Q: The value of f(z) = e² at z = 3 + 4i in terms of x + iy is O a. 1 O b. e cos 4+ie sin 4 O c. e*…

A: Given, We have to find the value of  fz = ez  at  z = 3+4i  in terms of  x+iy  .

Q: 2. Find the length of the asteroid x = cos't and y=sin't , 0<t<2n. x = cos' t y = sin³ t

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Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

Q: T/2 COS z xp V4 - sin? a

A: givenI=∫0π2cosx4-sin2xdxsubstitute  sinx=t therefore limits will change t=sinπ2=1  to t=sin0=0after…

Q: If the integration by parts was used to integrate the product of e^ax and sin(bx) and cos(bx).…

A: 1. To evaluate the integral ∫eaxcosbxdx+i∫eaxsinbxdx:

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

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Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2rtx) cos(50tt), where x…

A: Solution :-

Q: Evaluate f sin (3t) cos(3t)dt COS Select one: sin (3t) +C a. b. sin(3t) +C sin (3t) + C d. sin (3t)…

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Q: Determine c, and c2 so that y(x) = c, sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A: Consider the function: yx=c1sin 2x+c2cos 2x+1. Calculate c1 and c2. Given yπ8=0 and y'π8=2.   Since…

Q: a. Show that If z=x+iy where y >0 Then: 0 < |e*|<1 b. Evaluate cos (i z) – sinh?(z)

A: Using De Moivre's Theorem

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A: Given y (x) = c1 cos(x) + c2 sin(x)and y(0) = 1,   y'(π) = 1

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Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

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Q: The values of C, and C, so that y(x) = C, sin (2x) + C2 cos (2x) satisfies the following conditions:…

A: Solution:

Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: 3 Find cos(x+y), given that cosx= and siny = 2 3 TT <y<2n. 0<x< 2 Select one: V5-2/15 a. 10 b. None…

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Q: The cos'ydy is equal to 3 1 A. siny + sin³y + sin³y -; sin'y + C 5 3 B. siny – sin³y +sinsy -sin?y +…

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Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: 1 In AABC, AB = xcm, BC=(4- x)cm, ZBAC=y and ZBCA = 30°. Given that siny show that =D4(v2-1) (5…

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Q: dr Solve the given differential euation: + rtan 0 = 7cos0. de %3D r = (70 + C') cot0 Or = (70 + C)…

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Q: Find the length of the cardioid r = 1 – cos 0.

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Q: Find the area. a. Inside one leaf of the three-leaved rose = cos30 b. Shared by the circle r=2 and…

A: Given that a) r=cos(3theta) b) r=2 and r= 2 (1 +sin(theta)) c) r=-3cos and r=1-cos( theta) We have…

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Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

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Q: g(b). Use the Substitution Formula, -g'(x) dx = f(u) du where g(x) = u, to evaluate the following…

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Q: We have r(t) = (2e-t, sin-'t, In(1 –t)) , %3D Find 1- The domain 2- ar , an, T, N and t at t=1

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.