H.W.3: ExPress the fallowing functions by Cartesian ege 2-=1+2r Cosa 3- ra4 tan& seco tr=D4 Csc

Q: The curves T1(t) = (2t, t“, – 4t) and T2(t) = (sin(5t), sin(t), t) intersect at the origin. Find the…

A: Given that  The curves R1 and R2  Intersect at origin  To Find the angle between the curve

Q: your ans wers as comma-separe piaces wher Solution, enter NO SOLUTION.) 4 tan(e) + sec?(e) = 6

A: Given equation is  4tanθ+sec2θ=6 As we know that  tan2x+1=sec2x

Q: Find fx and fy, and evaluate at the given point.

A: Given fx,y=tan-1yx. To find fx and fy at point (2,-2). Solution: Partial derivative of a…

Q: Eliminate the parameter in the equations: x = 3 cot t and y = 3 csct %3D

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Q: A point P in the first quadrant lies on the parabola y = x2. Express the coordinates of P as…

A: To express the coordinates of P as functions of the angle of inclination of the line joining P to…

Q: Ex:57 Find the FisiE of the Juuctiou sin TIt ZL oくtくし - siu -Lくtく

A: Given, The formula for the Fourier series expansion is,

Q: Guide Question: 1.) From figure 1. what conclusion can be reached using converse of hinge theorem…

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Q: Given the parametric equations x = 2(8 – sin®) and y= 2(1 - cose). The slope of the tangent line to…

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Q: 21. r = 1- sen 0 22. r = 1+ cos 0

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Q: A. Sketch the two curves: 1. r1 = 3 cos 0. 2. r2 = 1+ cos 0.

A: Use polar system to sketch this curve.

Q: jw F(w). [a - acos (wr)] - A 1 Tjw jwF(W) = -2A (1-cos (WT)). Tjw jwF(W) = -2A (asin ² (WT)) Tjw How…

A: since we have a trigonometric identity:                                   cos(2θ) =1-2 sin2(θ)⇒ 2…

Q: Find the lengths of the curves 1.The curve r = cos^3 (u/3), 0<= u<= pai/4 2. The curve r =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find the lengthof the curve r = a sin? (0/2), 0seST, a>0

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Q: Q1 Find all the points of intersections of the curves r = 1+cos0 and r=1+sin r-1+(8) r=1+1)

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Q: cos(zt),nt, sin(nt)) e point where t = 0 to the point point where E1

A:

Q: If X =r cose equation (d ,y=r sin@ then show that the will be Erans formed into dy 2. 3D0 dr

A: Change of Variables: Suppose where and Then and

Q: b) r= 3cos(0)-3 sin (0)

A: Idea: substitute x=rCos(theta) and y=rSin(theta) and simplify we get equation in Cartesian form

Q: Find the measure of the given angle when given the value of one of its function. 1. Tan X = 7.22345…

A: We have to find the given angle measure in radians and degrees by using inverse trigonometric…

Q: Ex. 3. the horizontal plane through the point of projection. If a and B are the possible angles of…

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Q: Trace the curve: r = 1/2 sinꝋcos^3ꝋ.

A: The equation of the curve is r=12sin θcos3θ. First check the the symmetry of the curve. The curve is…

Q: The curves r1(t) (5t, t,- 2t') and 72(t) = (sin(- 4t), sin( – 3t), t - T) intersect at the origin.…

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Q: Express the function r = 4 cot 0 csc 0 by cartesian form

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Q: Pपा+ with a focus at co,-1) 'and directrix y=l

A: Vertex will be the midpoint of y=1 and (0,-1)  That is (0,0) So, (h,k)=(0,0)

Q: Find the sine, cosine and tangent, respectively, of z T. 10 8 6. 5 3 5 3' 4 4 3. 3. 5 5' 4 4.

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Q: If we ignore air resistance, then the range R(0) of a baseball hit at an angle 0 with respect to the…

A: Given:  Rθ=1gvo2sin2θ              for 0≤θ≤π2θishitting angle to a baseball.   G1:  0≤θ≤π2…

Q: C Reduction OF Crder and Variation OF Parame te 1. : tan 2x

A:

Q: 7] Find the area of the shaded region cleaned by the windshield wiper shown. 130° rcle T if the…

A: Qus no 7- we use sector formula and we solve and qus nom. 8,9,10,11 we find trigonometry function…

Q: Consider the parametric equations x sin 2t and y -4+c ost. which of the following dy7 represents 2…

A: We are given that x=sin 2t y=4+cos tWe need to find dydx

Q: The point P(2, -1) lies or (a) If Q is the point (x, 1/ the slope of the secant al places) for the…

A: Given the given curve is y=11-x and the given points are p2,-1 and Qx,11-x. Apply formula for the…

Q: Find the lengthof the curve r =. a sin? (0/2), 0 s 0s 7, a > 0

A: Arc length of curve.

Q: Ex: Two lines (y=1 a-d y-x1), Sind the equation of the linc that passes through the itersection…

A: If a line is y=mx+c , then mis the slope Angle between two lines is given by tanθ = ±m2-m11+m1m2 The…

Q: Question 3 Find the point(s) of intersection of the curves r = 6 and r = 12 sin e OA 6 * (6.5)(6) 3…

A: To find the intersection of the curve r=6 and r=12sinθ

Q: "Q2 → Sketch these funcion 3- 13 14 15 16 X + TT 2- Ysa4 cos( 17

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Q: The modified Eulerimethad 2 use to solue X 20s y=l Sined y at x=0.l, h=0.02

A: Modified Euler method or Heun's method is another method to solve an initial value problem…

Q: e* AY dy 'dy Ve? le?Y -16 ,2y

A: The given integrand is- ∫e4ye2y-16dy Substitute e2y-16=t to simplify the given integrand.…

Q: Show that the substitution 1- x a = -1, b = l+ 1, c = 1 2 converts the hypergeometric equation into…

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Q: Q8:- Find the intersection points between the given curves. r= cose 1- r= sin0 2- r= 3cos0, r=1+…

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Q: dr Find of r = (csc 0 + cot 0)-1? de

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Q: 1. If ß be the angle between the lines of regression, show that tan B = (1 -) 0,0/r (o, + o,).…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: Find the lengthof the curve r= a sin? (0/2), 0sesT, a >0

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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: In three-dimensional space, the graph of the equation z = sin(x) is: O a Line O a cylinrical surface…

A: Given,    Z= sin(x)    Sine curve is the curve of the sine function. It is also known as sinusoid.…

Q: 1bis a point in the Cartesia Plane Delermine 11) OB, 2) Cos B 113) CosecB 14 tan B 2)

A: Use the trigonometric identities and trigonometric ratios.

Q: What symmetries do these curves have?? r² = 1 – sin 0

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Q: Let ä(s) (a cos), a sin). then the normal plane equation is: X-a None y-0 .d O

A: normal plane equation

Q: Find the Cartesian equation of the curve: x = 2cos(theta) y = 1 + sin(theta) where theta is…

A: Given that the equation of the curve, x=2cosθy=1+sinθWhere,  0≤θ<π2

Q: Consider the following. x = tan?(0), y = sec(e), -1/2 < e < n/2 (a) Eliminate the parameter to find…

A: x=tan2(θ) and y=sec(θ) knowing that tan2(θ)=(tan(θ))2=sin2θcos2θ and that…

Q: from Equation (3). Then find the length of the indicated portion of the curve. 11. r(t) = (4 cos t)i…

A: The arc length is, 5π/2   The detailed solution is as follows below:

Q: The curves r1(t) (- 5t, t°, t*) and 72(t) (sin(5t), sin(2t), t) intersect at the origin Find the…

A: Find the thetha