For r=sin40, (i) sketch the curve. (ii) Find the area of one loop of the curve.

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

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Q: The curve ver = V1 + sin20.

A: Solution :-

Q: Find the arc length of the curve from z = 3 to = 6. Leave your answer as a simplified radical. f(x)…

A: Explanation of the answer is as follows

Q: Find the arc length of f(x) = (1+2²) from x = 0 to x = 2. Simplify your

A: Given :fx=231+x232x from 0 to 2

Q: Eliminate the paranoter t from the follewing S r(1) = 4+ sin t lu(t) 3- cost

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Q: Find the length of the curve y=Arc sin e^x when y= pi/6 to y=pi/2

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Q: Find the arc length in the second quadrant of the curve x23 +y2/3 = 25 from x = - 125 to x = – 8.…

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Q: Find the exact area inside the curve defined by r = 2 + 3 sin 0 and outside the circle r = 2.

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Q: Find the arclength of the curve a = 8 cos(3t), y = 8 sin(3t) with 0 < t<. 9

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Q: 3. Find the area under one arch of the curve y = sin(2r).

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Q: Find the length of the curve y = ln(sec x ), x is an element of [0, pi/4]

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Q: Find the area inside the curve r 12 = sin 20. %3D

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Q: Find the exact arc length of the curve. x6 + 8 y = from x = 1 to x = 3. 16x2 Give the exact answer…

A: To Determine: find the exact arc length of the curve  Given: we have a function y=x6+816x2…

Q: Find the length of the arc of x²+y²=64 from x=-1 to x=-3, in the second quadrant.

A: Given curve: x2+y2=64

Q: a²z a2z If z = arctan (2), find ду?

A: It is given that z=arctanyx z=tan-1yx

Q: The arc length of the portion of the curve y =ex with 3 <x<5 is

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Q: The tangent to the function y= csc x at x= π/4 and the x- and y- axes form a triangle. Find the area…

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . 4

A: Given that, y = ln(cosx) To find length of curve, we have formula Length of curve = ∫ab1 + [f'(x)]2…

Q: Find the length of arc of the curve 6xy = x^4 + 3, from the point where x=1 to the point where x=2

A: The given curve is: 6xy=x4+3 y=x46x+36xy=x36+12x Differentiate it: dydx=3x26-12x2dydx=x22-12x2

Q: Find an interval of t-values such that c(t) = (cost,sin t) tracesthe lower half of the unit circle.

A: Consider the given point as ct=cost,sint

Q: Find the length of the curve y = ln (sec x), 0&lt;= x&lt;= pai/4

A: Given,

Q: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

Q: Find the arc length of the curve r = 2/0, for 7/2 < 0 < T Arc length =

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Q: Q2/Find the length of the curve r = sine + cose between

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: The given question is the application of integration and solved as shown in step2.

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: Find the exact length of the following curve y = Vx – x² + sin-'(/T).

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Q: Find the length of the curve y = ln (cos x), 0&lt;= x&lt;= pai/3

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Q: The arc length of the the curve x =V9 - y2 - 3<y<3 is equal to Select one: О Зл O 9T О бл 18T

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Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

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Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: Find the arc length of y (x + 7)3 + (x + 7)-1 for 1 < x < 2. (Give your answer to three decimal…

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Q: 1 for the interval [1,3]. 8x2 Find the arc length L of the curve y

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Q: ind all the tangents to the curve y cos (x %3D

A: Here we have to find the tangents on the curve y=cos(x+y)...........(1)     , -2π≤x≤2π parallel to…

Q: Find the arc length of the graph of the function over the interval. y = In(sin z);

A: Given,          y=lnsinx ; π4,3π4

Q: Find the length of the curve y=In (cos x), -≤x≤0. The length of the curve is. (Type an exact…

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Q: Find the length of the curve r = 4 – 4 sin 0

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: To use the geometry we will change the polar equation into the cartesian equation first.  For that,…

Q: Find the arc length of the graph by partitioning the x-axis.   y= ln(sin x), from x = pi/6 to x=…

A: Let fx be a smooth function over the interval a,b. Then arc length of the portion of the graph fx…

Q: Find the exact length of the cur curve. y = Vx- x2 + - sin (V)

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Q: Find the length of the arc of the curve x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant

A: The curve in the second quadrant can be represented as, x2+y2=64y=64-x2   The derivative of the…

Q: dx L% = 1+ dy dy

A: Given equation of curve; y  = (x/2)3/2 , x = 0 to x = 2

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

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Q: Find the exact area between a large loop and the enclosed small loop of the curve r = 1 + 2 cos(30).…

A: (1).    The given curve is: r=1+2cos3θ

Q: Solve for X and determine the arc measure of GF

A: We would use the central angle (60) to find the length of arc and x.

Q: If x = 10 cos 0 and y = 10 sin 0, find the total length of the curve swept out by the point (x, y)…

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.