Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in rectangular coordinates for the curve r=4cos18θ. (x^2+y^2)^2 = ?

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Q: If cosh x  =5/3 and x>0 , find the values of the other hyperbolicfunctions at x .

A: Given  cosh x  =53 , x>0

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Q: |x = 3 sin´ (3t ) +1 ;teR = 2 cos (3t)–1

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Q: Find the slope of the tangent line to the curve cos(За — Зу) — ае -37/2 2 at the point (37/2, 27).

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A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Find length of arc of the curve 9y2=4x3 from the origin to the point (3, 2√3)

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Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: 1. Use implicit differentiation to find an equation of the tangent line to the hyperbola - * = 1 at…

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Q: Find an equation of the tangent line at the point specified.

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Q: Plot the astroid x = cos3 θ, y = sin3 θ and find the equation of the tangent line at θ = π/3 .

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Q: sin(7x) + sin2(7x),  (0, 0

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Q: Can you please give me two points from the topologist's sine curve?

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Q: Find the equation of tangent line of curve That is given by parametric equations x=3cost+sint y=e2t

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A: Derivative y with respect to x and then substitute the given point to find the slope.

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Q: Show that the curve  x = 3 cos(t), y = 5 sin(t) cos(t)  has two tangents at (0, 0) and find their…

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Q: What is the slope of the tangent line to a curve with parametric equations of x= 2t+1 and y= 3t-1? *

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Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

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Q: Show that the topologist's sine curve is not pathwise connected

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Q: Estimate sin (31) using an appropriate tangent line to the graph of y = sin(x).

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Q: Compute the length of the curve r-4 sin 26 for Approximate to three decima places.

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Q: Find an equation of the tangent line at the point indicated.

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Q: the length of the curve y = coshx 1<= x <=2 is sish (2) - sinh(1) Select one: True False

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Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

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Q: Find the equation of the tangent line to the parametric curve

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Q: Find the slope of the tangent line to the curve 5 sin(z) + 4 cos(y)- 5 sin(z) cos(y) + z = 3x at the…

A: Consider the curve  5sinx+4cosy−5sinxcosy+x=3π

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Q: Find the slope of the tangent line to the curve  5 sin(x) + 2 cos (y) - 5 sin(x) cos(y) + x =5π at…

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Q: Find the exact length of the curve. y = In(sec(x)), 0≤x≤ w|ले

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