If v x w = (-1, 4, 0) and v · w = 4, find tan(0), where 0 is the angle between v and w. tan(0) =

Q: With the aid of residues, and a carefully chosen contour, show that d.x x5 +1 5 sin(T/5)

A: We we solve the general form of the integral for n instead of 5 Then we will substitute n=5 in order…

Q: Find əw/ar and aw/as when r = n and s = 0 if w = sin(2x – y), x = r + sin s, y = rs.

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Q: If w = f(x, y) and x = r cos θ, y = r sin θ, find formulas for ∂w/∂r, ∂w/∂θ, and ∂2w/∂r2.

A: Answer(1): Given that, w = f(x, y)  and  x = r cos θ, y = r sin θ Now, to find formulas for ∂w∂r,…

Q: If sin(x + y) – sin(x – y) = 2f(x) sin y, then f(x) is equal to C. tan x D. cos? x A. sin c B. cos x

A: Trigonometric functions are also known as circular functions. They can be defined as the functions…

Q: a) Show, from 1st principles, that if a small angle x is measured in radian, then: i) ii) sin x = x…

A: take a triangle as below :

Q: If x = e" tan v, y = e" sec v, then the value of y%3D X +y X- +y is

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Q: Verify the following, for the two angles alpha (a) and beta (B) sin(a-B tan a tan 3 cOS O cos R

A: To verifysin(α-β)cosαcosβ=tanαtanβ

Q: The functions 7(t) = (cos t, sin t) and R(t) = (cos(t²), sin(t²)) generate the same set of (x, y, z)…

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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: Find the angle(s) that satisfy the given values in the interval (0, 2r) 1. cos I = 2. secz = V2 3.…

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Q: If x= cos 50 and y = sin 50 , then dx 18 %3D a. - cot 50 b. - 5 cot 50 C. 5 tan 50 d. -5 tan 56

A: Differentiate both equations x & y separately and take their ratio.

Q: If sin(x + y) – sin(x – y) = 2f(x) sin y, then f(x) is equal to C. tan x D. cos? x A. sin c В. cos x

A: Given; Sin(x+y)-Sin(x-y)=2f(x)Siny

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f;(5,5,0).

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Q: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: Determine the exact measure(s) of 0, where 0° < 0< 360°. and tan 0 = 0

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Q: b) Describe, the motion of a particle with position (x,y) as t varies in' tthe given interval X= 5+…

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Q: e cos(t), and e sin(t).

A: Given: f(t)=e-tcos(t)andf(t)=e-tsin(t)

Q: If u = tan- the value of x2 +y? +xy du du at x = 1 and y = 3 is

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Q: Use the given conditions. tan(u) = -3/4, 3t/2 < u < 2n (a) Determine the quadrant in which u/2 lies.…

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Q: Find y" given that sin(y) + cos(r) =I %3D

A: We have to find the second derivative

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: If y = sin(msinx) then show that (1– x)' y, – xy, + m² y =0.

A: Given: Given y=sinmsin-1x We want to show that 1-x2y2-xy1+m2y=0

Q: solve for the angle u, where 0 … u … 2π sin 2θ - cos θ = 0

A: To calculate the angle u

Q: B. FIND THE FOLLOWING ANGLES, WHICH LIE BETWEEN O AND 90°: (d) Cos 1.000 (e) Tan 0.500 (f) Tan 8.500…

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Q: Let W= x tan Cy?) Find : dw

A: We will find out the required value.

Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

Q: Use Figure 22 to find all angles between 0 and 2π satisfying the given conditions.

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Q: Let P = {x € R | sin(x) = 0} and Q = {na | n E Z}. What is the relationship between P and Q?

A: Let P = {x ∈ R | sin(x)=0}, and Q = {nπ | n ∈ Z}. What is the relationship between P and Q​

Q: If z = x2 + y? x = e' cos(s) and et sin(s y = ), then

A: ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s Lets find out each derivative z=x2+y2∂z∂x =2xx=etcos(s) ∂x∂s=et…

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f:(5,5,0).

A: This question is based on Partial derivatives.

Q: a) Find dz, if z = e' sin e %3D b) Verify uxy = uyx , if u = In /x² + y² . %3D

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If sin x + b? cos x = r cos (x + a), where b e 0} and a and r are positive constants, then r and tan…

A: We will find out the required values.

Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: 1 Given that P = 2a, – ay 2а, - Q = 4a, + 3a, + 2a, R = а, + a, + 2a, find: (a) |P + Q – R|, (b) P·Q…

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Q: Find ∂w/∂r and ∂w/∂s when r = π and s = 0 if w = sin (2x - y), x = r + sin s, y = rs.

A: Given w = sin (2x - y), x = r + sin s, y = rs

Q: Assume that x, y ER and z = x + iy E C and answer the followings: 1. Evaluate sin(i) =?, cos(i) =? ,…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

Q: Given tan x = sin x < 0; cos y = csc y < 0, find sin(x-y) 3/5

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Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

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Q: Find Z, , Zy, Zy, Z, for the following equation: ху, Z= a x +cy° + c sin(xy) + d cos(y?), where…

A: We have given Z = a x3 + c y3 + c sin(xy) + d cos(y2)  Where a,b,c,d are constants)

Q: For an angle x, sin(x) = 4/17. Find the following: %3D cos(x) = %3D tan(x) = csc(x) = %3D sec(x) =…

A: Given,sin(x)=417we know that,sin2x+cos2x=1cos2x=1-sin2xSubstituting value of…

Q: akoy that the product of the perpendiculars drawn from the two points (t Va-b,0) upon the line cos 0…

A: We have to show that product of of perpendiculars is b^2.

Q: Given, a(x,y,2) = 23x3 tan (y) + x*29 %3D Find the expression for Izyz and Caleulate it at the point…

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Q: given z=x2-y2, x=r cosθ, y=r sinθ, find ∂z/∂θ

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

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Q: Convert to rectangular coordinates. x = 1+ sin t, y = 1 + cos t for t in 0, 27

A: The solution are next step..

Q: If sin t 2 and t is in the 3rd quadrant, - then cos t = Vī6 V34 5 Vī6 3 Vī6 | Vī6 3

A: Given Sin t=-(3/5) t =is in the 3rd quadrant Find out  cos t=?

Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

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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

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