Find the Cartesian equation of the image of the line x = 2 under the mapping z → sin(z)

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 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: 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: Plot the curve r = 1+sin 8. Then find the length of the curve.

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Q: A bullet fired from a gun follows the trajectory x = at, y = bt – 16t2 (a, b > 0) Show that the…

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Q: Sketch the graph of r = 1–2 cos 0. Find tangents at the pole, all vertical and horizontal tangents.

A: Consider the given equation of graph.

Q: Find the slope of the curve r=7-cos(theta) at theta=9pi/4.

A: I am attaching image so that you understand each and every step.

Q: Trace the curve r^2 = 4 cos^4 θ tan^2 θ and Identify different points. [HINT: Use 0°, 15°, 30°,…

A: Given that, r2=4cos4θtan2θ

Q: Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular…

A: We have to show that cos12θ=cos34θ−3cos4θsin24θ Consider  cos12θ=cos34θ=cos3P        Let P=4θ We…

Q: r = 2 sen 0, 0 = "/6 15.

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Q: Trace the curve r= 1/2 sin(theta) cos^3 (theta)

A: Given curve is: r=12sinθcos3θ ⇒r=142sinθcosθcos2θ=14sin2θ1+cos2θ2=18sin2θ+18sin2θcos2θ Here replace:…

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: Give the center and radius of the circle generated by the equations x = 3 sin t, y = -3 cos t, for 0…

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

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Q: Using the polar function r = 1 + cos(θ), find the slope of the tangent line at the point (3/2, pi/3)

A: Given: The polar function is, r=1+cosθ

Q: From the information given, find the quadrant in which the terminal point determined by t lies.…

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Q: Find the equation of a sine wave in the form y = a sin(x + c) + d that is obtained by shifting the…

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Q: Please help

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Q: Let P(x, y) be the terminal point on the unit circle determined by t. Then sin(t) = , cos(t) and…

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Q: Find the acute angle to the nearest degree between the vertical lin x = 2 and 3x -2y + 1= 0

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Q: Find the angle 0 between w = cos 플 i+ sin푸 7 cos플 i + sin and %3D

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Q: Find the equation of the tangent plane R(a, b) = to the surface at the point that corresponds to a…

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Q: The curves T1 (t) = (3t, t°, – 4t°) and r2(t) = (sin(5t), sin( – 2t), t) intersect at the origin.…

A: We have to find the direction vector first.

Q: Match each angle on the left with its corresponding reference angle on the right. Unit Circle (cos,…

A: To match the given angles with the given reference angle.

Q: Show that r = a cos θ + b sin θ is the equation of a circle passing through the origin. Express the…

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Q: Find equations for the tan-gent and normal lines to the curve y = 1 + cos x at the point (pai/2, 1).…

A: Given curve is,

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: Find the angle  (in radians and degrees) between the lines. Round your answer to four decimal places…

A: If two non perpendicular lines have slopes m1 and m2 then the angle between these two lines is given…

Q: Sketch the following curves and find the points of intersection of the pairs of curves. a) r=…

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Q: Use a calculator to find the acute angles between the planes into the nearest hundredth of a radian.…

A: Explanation: Given planes are: P1: 2x+2y+2z=3P2: 2x-2y-z=5 and its vector  n1=2,2,2n2=2,-2,-1

Q: r = -3 cos(20) – cos(0) os(e)

A: To check the symmetry of the curve  r=-3 cos 2θ-cos(θ)...(1) with respect to a straight line θ=0 or…

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric equation is x=cos 2t,   y=sin t,    -π≤t≤π. This implies that, x=cos…

Q: Find sin u and cos u if the given point lies on the terminal side of u.     (3,-4)

A: R=x2+y2sin u= y/Rcos u=x/R

Q: Find the angle between two lines having slopes of 1, and 1/2 respectively. (A) sin (B cos (c) sec D…

A: In this question, we need to find the angle between two lines having slopes 1 and 1/2 respectively.

Q: Find the angle (in radians) between the line with equation F(t) = +t and the line with equation…

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Q: Find the equation of the line in the xy-plane that goes through the origin and makes an angle of 1.7…

A: Given in xy plane line pass through origin and make angle of 1.7 radians with positive x axis.

Q: Suppose the angle formed by the line y = 2x and the positive x-axis is 8. Find the tangent of 8.…

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Q: Identify the curve by finding a Cartesian equation for the curve.17. r = 5 cos θ

A: We need to find the curve by finding a Cartesian equation. Here,  r = 5 cos θ. Let us take x=r cosθ…

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: A cyclist is travelling in a straight path at a constant speed along a dirt road with a button stuck…

A: Given: The equations of a cycloid x=rt-sin t, y=r1-cos t.

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: Suppose that y is an angle with tan y = 11 and y is not in the fourth quadrant. Compute the exact 9.…

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Q: Use a calculator to find the acute angles between the planes into the nearest hundredth of a radian.…

A: Angle between two planes a1x+b1y+c1z+d1=0 and a2x+b2y+c2z+d2=0 is,…

Q: The point P on the circle x2 +y² = r² that is also on the terminal side of an angle 0 in standard…

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Q: From the information given, find the quadrant in which the terminal point determined by t lies.…

A: To find the terminal point t lies. a  sint&lt;0  and cost&lt;0b  sint&gt;0  and cost&lt;0c…

Q: Sketch the graph and the curve represented by x = 3 cos 0 and y = 4 sin 0 ,0 < 0 < 2n by eliminating…

A: The given parametric equation,      x=3cos θ and y=4sin θ, 0≤θ≤2π

Q: Find tan theta if theta  is the angle formed by the line y = mx and the positive x-axis

A: We need to find tanθ for the given equation of line