(a) Let A, be the area of a polygon with n equal sides inscribed in a circle with radius r. By dividing the polygon into n congruent triangles with central angle 2n/n, show that the following is true. A, = n? sin(2 kle

Q: 1. Find the area of the part of a petal of the four leafed rose r = circle of radius . | cos(20)|…

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Q: 80. Show that the area A of the triangle is given by A = - bc sin A. 2 a B

A: Let h be the height of the triangle, then

Q: Find the area of the region inside the circle r = 2 sin (θ + π/4)and above the line r = sec (θ −…

A: Given : Circle   r=2sinθ+π4 and Line  r=secθ-π4   We have to find the Area of the region inside the…

Q: Find the area of the intersection of the circles r = sin θ andr = cos θ.

A: Given: r=sinθr=cosθ

Q: 1) Find area inside the circle r= 4cuse and to the right of line r = sece %3D

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Q: Find the areas of the regions Inside the circle r = 4 sin θ and below the horizontal liner = 3 csc θ

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Q: 2. An inverted conical water tank with a height of 12 ft and a radius of 4 ft is drained through a…

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Q: If the area inside both the cardioid r = 3+3 sin 0 and the circle r = 3 is A+B÷, then what is A+ B?…

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Q: Consider the quarter-circle of radius 1 and right triangles ABE and ACD given in the accompanying…

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Q: 2. Consider a circle centered at the origin with radius r. Use trigonometric functions and…

A: Explanation of the answer is as follows

Q: Consider a triangle with sides 3 cm, 4 cm, and x cm. Let a be the included angles of the sides with…

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Q: Consider the quarter-circle of radius 1 and right triangles ABE and ACD given in the accompanying…

A: Here the objective is to prove the identity given below:

Q: *6. In the figure, the larger circle, centre O, intersects the smaller circle at P and R. Q is…

A: Given that the larger circle with center O, intersects the smaller circle at P and R. So, OP, OR are…

Q: The base of a solid is the region between the curve 16 sqrt ( sin x) and the interval [0,pi] on the…

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Q: 5. Find the length of the arc of a circle of radius r subtended by the central angle 0. Round the…

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Q: 1. Given a circle of radius 7 in and a central angle of 116°, find: a) The arc-length subtended by…

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Q: Find the area shared by the circle r, = 9 and the cardioid r, = 9(1 - cos 0). .....

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Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: Consider the quarter-circle of radius 1 and right triangles ABE and ACD given in the accompanying…

A: From the given fig. Using standard area formulas, We need to show that…

Q: Consider a triangle with sides 3 cm, 4 cm, and x cm. Let 0 be the included angles of the sides with…

A: 1 is an answer.

Q: If the area enclosed by the curve a = 7 cos t and y = 7 sin t (where t e R) is A, then what is A?…

A: If the area enclosed by the curve x=7cos^3t and y=7sin^3t (where t∈R) is Aπ8, then what is A?

Q: On a circle with radius of 10 cm, find the length of the arc that subtends the central angle of 72.…

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Q: The “strophoid” is given by r=2cos(theta)-sec(theta) for -pi/2 < theta < pi/2 Find the exact value…

A: r(θ) = 2cosθ - secθ   when θ∈-π2,π2

Q: Consider the four petaled rose r = sin(2θ). Find the area of one leaf, then prove that the total…

A: Given four petaled rose r=sin(2θ). We need to find the area of one leaf. First let us sketch the…

Q: Find the area of the region common to the circles r=-6 sin 9 and r= 3.

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Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: - The area of a circle with radius r is The area of a sector whose measure of the arcs is a/an A of…

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Q: 2. ind the length of an arc of the cycloid given by, x = a(0 + sin0), y = a(1 + cos0), Ar

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Q: B Use the given right triangle to find ratios in reduced form, for sin A, cos A, and tan A 3 A. sin…

A: If all (three) the sides of a right angle triangle are given then all the trigonometric functions…

Q: The lower right-hand corner of a long piece of paper 6 in wide is folded over to the left-hand edge…

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Q: Find the area of the region shared by the curves r = 4 and r= 4 - 4 cos theta, as shown in the…

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Q: On a circle of radius r, a central angle of u radians subtendsan arc of length s = ; the area of the…

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Q: 29. Area = %3D EF, FH, and HI are tangents. EI is a diameter. E 2ft.F J 8ft. H

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Q: Consider a triangle with sides 3 cm, 4 cm, and x cm. Let 0 be the included angles of the sides with…

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Q: 34. In O P shown, it is possible to determine that arc FG = arc DE. G D P F E True False

A: Solve for the true or false

Q: 1. Show using similar triangles that tan 0 and cot 0 are the respective measures of line segments AR…

A: Using figure ,∠QOA + ∠QOB = 90°⇒θ+∠QOB = 90°⇒∠QOB = 90°-θIn ∆QBO ,∠QBO = 90° and ∠QOB=90°-θ ⇒∠OQB =…

Q: If the area inside both the cardioid r = 6 + 6 sin 0 and the circle r = 6 is A+ B² then what 4 is A+…

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Q: If the area inside the cardioid r = 6 – 6 sin 0 and outside the circle r = 6 is T+ 8 A · then what…

A: To solve the following problem

Q: If the area inside both the cardioid r = 6+ 6 sin 0 and the circle r = 6 is A+ B¨, then what is A+…

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Q: . A central angle u is drawn in a circle of radius r, as in thefigure below.(a) The length of the…

A: Given: A central angle θ is drawn in a circle of radius r. To find: The length of arc and the area…

Q: y = sin x 2

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Q: Consider a triangle with sides 3 cm, 4 cm, and x cm. Let a be the included angles of the sides with…

A: Here, a=3, b=4 and C=aUsing the formula to find the area of the triangle,A=12ab sinC   =12(3)(4)…

Q: show that the area An of an n-sided regular polygon in a circle of radius r is An = ((n.r.r)/2)…

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Q: An arc PQ of a circle subtends a central angle 0 as in the figure. Let A(0) be the area between the…

A: Since PR is tangent so PR is perpendicular to OP where O is the center.  Thus, PR=r×tanθ2.…

Q: In the Figure, CB is a diameter of a circle with a radius of 2 cm and center O, A ABC is a right…

A: Solve for sin a

Q: A corner has been cut out of a 5 in by 3 in rectangle. The removed corner is in the shape of a…

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Q: In a right triangle ABC, right angled at C, if tanA = 1 , then verify that 2sinA cosA = 1

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Q: In Oo, radius OD chord AB at point C. If OD = 5 and AB = 8, find OC. O 3.5 0 3 4 O O 39

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Q: Find the area of one leaf of the "four-petaled rose" r =7 sin 20 shown in the following figure: r=,,…

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Q: Starting with a 20-foot-long stone wall, a farmer would like to construct a rectangular enclosure by…

A: The rectangle is of length= x+20 feet And width = w feet20 feet of the perimeter is stone wall. So…