Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular coordinates for the curve r = 5 cos 120. = (2² + y²)²

Q: a. Express x = --3-8ż in its trigonometric form r (cos(0) + i sin(0)) with 0 ≤ 0 < 2. Give your…

A: a) x=-3-8ib) 2+5i2+2i

Q: Determine the period of the sinusoidal function y = 0. 75 cos 7x – 0. 5.

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Q: ) Write the equation r2+r(sin 0-6 cos 0) = 0 in Cartesian coordinates and identify the corresponding…

A: Solution is given below:

Q: The parametric equations: x = a a cos 0,y = a sin 0;0 ses 2n, define a curve called an asteroid

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Q: The curves 71(t) = (4t, tº, 2tª) and 72(t) = (sin(4t), sin(5t), t – ) intersect at the origin. Find…

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Q: The curves 71(t) = (2t, t°, – t) and 72(t) = (sin(3t), sin(2t), t – 7) intersect at the origin. Find…

A: Given : The curves r1(t)→=2t,t6,-t2   and  r2(t)→=sin(3t),sin (2t),t-π intersect at origin(0,0,0).

Q: 1. The parametric equations: x = a cos 0,y = a sin? 0;0 ses 2n, define a curve called an asteroid

A:

Q: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Given x and y values.... Let us find dy/dx to draw the graph....

Q: The curves 71(t) = (5t, t°, - 4t) and 72(t) = (sin(t), sin(3t), t – ) intersect at the origin. Find…

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Q: Find all the points of intersection of the curves r=cos3θ and r=sin3θ.

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Q: Graph these parametric equations on the TI and include screenshots x = 2t – 2 sin t, y = 2 – 2 cos t…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

Q: Beats Express cos 3t - cos t in the form A sin at sin ,Bt, and sketch its graph.

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Q: The graph of the curve given by the parametric equations X=sint and y=cos2t IS à Select one: O ircle…

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Q: B. With the indicated conc the given equation. 2. 2 Cos2 0 = -3 Sin 0, 3. Tan? x- Secx = 1, 4. Cos…

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Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: Show that Cos210 cos 70 - 3cos7@sin?78 and use this identity to find an equation in rectangular…

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

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

Q: Sketch the curve and Find the length if the curve: x=cos(2t), y=sin(2t), 0<_t<_ pi/2

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Q: If 0 be a positive acute angle satisfying cos² 0 + cos“ 0 = 1 then the value of tan² 0 + tan“ 0 is

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Q: Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

A: To find the Cartesian equation of the given curve.

Q: Eliminate the parameter to find a Cartesian equation of the curve, and sketch the curve and indicate…

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Q: 1. Find a cartesian equation for the curve r² sin 20 = 8.

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Q: Find the exact length of r = 3 sin 0 + 4 cos 0. II

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Q: Write the equation of the line tangent to the graph of r : 4 cos 0 when 0 = ". %3D %3D

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Q: Find the smallest positive angle such that sin 2a = cos 3a %3|

A: As per our guidelines we can solve only one question. Rest question can be reposted.  Here in…

Q: A player hits a ball from the ground with an initial velocity of 85 feet per second at angle \theta…

A: Given that, In a projectile motion, Initial velocity (v) = 85 feet/second Angle is θ. and  cosθ = 13…

Q: 8. 8 sin 0 at the point (9 Find the slope of the tangent line to polar curve r = 6. Submit Question

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Q: 3. Suppose that 0 is an angle in standard position whose terminal side intersects the unit circle at…

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Q: The magnitude of A = p cos 0 a, + pz2 sin Ø a, at point (3, -4, 0) is: %3D

A: To find magnitude of A⇀=ρcosθaρ⇀+ρz2sinφaz⇀   at point (3,-4,0)

Q: 6. A parametric equation is given by x=1.5 sin (5t), y-1.5 cos (3t), Plot the function for 0<ts 2a.…

A: To plot the graph

Q: Express cos { θ + π/2 ) and sin { θ + π/2 } ) in terms of cosθ and sinθ.

A: Given  cosθ+π2, sinθ+π2

Q: 1 200 -1 1 What is the value of the -coordinate of point A?

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Q: Determine COs x-2 = 0. correct to four decimal places, a root OF the equation sin X+3 %3D

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Q: 270° -1 | -1

A: Option E Sin(270degrees) is correct answer.

Q: Write an equation for the line tangent to the graph created by the parametric 3 cos 0 and y(0) = 3…

A: To find the equation of tangent line.

Q: . The curve with parametric equations x = (1 + 2 sin 0) cos 0, y = (1 + 2 sin 0) sin 0 is called a…

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Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: 3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

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Q: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Solve by finding slope

Q: 2. The terminal side of angle 0 in standard position goes through the point (-1,-5). a) sin(0) b)…

A: Recall the following. If the terminal side of the angle θ that passes through the point x, y, then…

Q: Show that cos 3θ = cos3 θ − 3 cos θ sin2 θ and use this identity to find an equation in rectangular…

A: Show the given identity:

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: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Please check step 2 for the solution.!

Q: v in the quadrant IV COS (U+V)=

A: we have to find the exact value of cos(u + v) given that sin u=-3/5 with u in quadrant III, and sin…

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&lt;π2

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

Q: jw F(w). 2 - TAN [* - ACOS(WT)] acos Tjw jw F(W) = -2A (₁ - cos (WT)). Tjw jWF(W) = -2A (asin" (WI))…

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Q: The parametric equations: x =ac a cos³ 0,y = a sin 0;0 <0s 2n, define a curve called an asteroid

A: Please refer the attached image for complete solution. THANKYOU.