Suppose r(t) = (et cos t)i + (et sin t)j. Show that the angle between r and a never changes. What is the angle?

Q: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

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: Tan Be Xe O de d Bo find

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Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: If z = f(x, y), where x = r cos 0 and y = r sin 0, show that a²z 1 a°z 1 əz r дr дх? dy? дr?

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Q: Let y = (sin z+ cos r)e", x E [0, 27]. %3D

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Q: In AXYZ with a right angle at Y, the cosine ratio can be used to find the length of XZ as O a) XY…

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Q: If y(u) J5 COs v9 dv then cos(9u eIu y'(u) = %3D e4

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Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

Q: If z = cos (r + cos y), show that az Fz ar ərðy dy dr

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Q: Suppose that r(t) =. Then the speed is

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Q: et u = e Sin P= sin sc Lind su using chain Rule

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Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

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: 2 = e" cos u = e – r, v= re".

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Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3 %3D

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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: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: What are the best choices for u and dv in evaluating  ∫ x cos x dx?

A: Given: I=∫xcosxdx for evaluating given integral, we will use integral by parts method according to…

Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

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: et sin t? blas Y - et cos t? lio -n/2 <t < 0

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Q: if y=sin(x), z=cos(x), v=y+x, where (-100 ≤x≤ 100) could you plot y, z, v

A: Given:- we are provided with three functions y,z and v where y=sin(x)z=cos(x)v=y+x=sin(x)+xNow, we…

Q: If r (t) = (cos(t), sin(t), 2) r(t) = (cos(t), sin(t), 2) , %3D T then fr (t) dt =

A: It is integration using limit problem.

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: Find the length of the curve. r(t) = (9t, 3 cos(t), 3 sin(t)), -5 sts 5

A: To determine the length of the curve.

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: Let t be the angle between 0 and such that sin t Then cos t sin(-t) cos(-t) tant =

A: Solution ) sin t = 1/4    t = sin-1(1/4)    t = 14.48 Cos (14.48) = 0.968 Sin(-t) = - sin t Sin (-t)…

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: If r (t) = (cos(t), sin(t), 2) , then ſr (t) dt =

A: r(t)=&lt; cos(t), sin(t) ,2&gt;

Q: Use Green's theorem to evaluate $y – sinx)dx + cosx dy Where c the triangle of the adjoining figure…

A: Green`s Theorem:-  Green`s Theorem states that the line integral is equal to the double integral of…

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

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Q: Consider the curve y(x) = sin x. Which one of the following statements is true?

A: sinπ2 = 1

Q: F k d

A: Use conic section we can prove it.

Q: Let r(t) = (sin 3r, cos 3r, /īt), Find T(t) and N(t)

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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: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: Find the length of the cardioid r = 1 + sinθ

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

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Q: If sint = - - and t is in the 3rd quadrant, then tan t %3D V45 45 O V45 V45 2 V53 O O O

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Q: If the angle at which the radius vector cuts the √√²-a² 2 1 a curve 0 = COS be o, then a r cos o…

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Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: Find T, N and k for r(t) = (e' cos t)i + (et sin t)j + (e)k

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Q: Given u= sin (r/t)+ ln (t/r)show that t(∂u/∂t)+r(∂u/∂r)=0

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Q: If the wronskain w(f,g)=cost + sin t, find Wu,v). Where : u(t) = f (t) +4g(t), v(t) = f(t)–3g(t) %3D

A: Given that Wronskian W(f,g) = cost+sint  We need to find W(u,v) , where u(t)=f(t)+4g(t) and v(t)=…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.