Math

Circle

1. Calculate the circumference of each of the circles at the right. C = 2tr 3 2. Calculate the ratio of the circumference to the radius for each circle, Explain why the ratio is the same for both circles.

The quantity that you found above is called a radian, and it is used for measuring the size of an angle. 5. Each of the sectors shown at the right are % of the circle. What is the subtended angle measure in radians? In degrees? Show all of your work.

The chord of circle x2 + y - 6x-8y = 0 passing through (0,0) and having positive slope, subtends an angle tan at the point where the circle meets the positive y-axis has the equation ax + by =0 then 3a + b} is equal to (where a, b are coprimes) Your answer

* the lines 2x + 3y + 1 = 0 and 3x - y - 4 = 0 lie along diameters of a circle of circumference 108, then the equation of the circle is O x2 + y2 + 2x + 2y - 23 = 0 O x2 + y2 + 2x - 2y - 23 = 0 O x2 + y2 - 2x - 2y - 23 = 0 O x2 + y2 - 2x + 2y - 23 = 0

9 15. The diagram below shows the unit circle. A. Determine the coordinates of Point C in terms of cosine and sine of e. D C B. Describe the relationship between Points C and D. What transformation(s) could be applied to Point C to get Point D? no C. Determine the coordinates of Point Din terms of cosine and sine of e.

9 15. The diagram below shows the unit circle. A. Determine the coordinates of Point C in terms of cosine and sine of e. D C B. Describe the relationship between Points C and D. What transformation(s) could be applied to Point C to get Point D? C. Determine the coordinates of Point Din terms of cosine and sine of e. D. Determine the coordinates of Point D in terms of cosine and sine of . E. Determine o in terms of e. F. Knowing that both forms of the coordinates to Point D must be equivalent, what can you conclude about the relationship between cos(180 - 0) and cose? The relationship between sin(180 - 0) and sine?

15. The diagram below shows the unit circle. A. Determine the coordinates of Point C in terms of cosine and sine of e. C B. Describe the relationship between Points C and D. What transformation(s) could be applied to Point to get Point D? 0 C. Determine the coordinates of Point Din terms of cosine and sine of e. D. Determine the coordinates of Point D in terms of cosine and sine of o. E. Determine o in terms of e.

9 15. The diagram below shows the unit circle. A. Determine the coordinates of Point C in terms of cosine and sine of e. C B. Describe the relationship between Points C and D. What transformation(s) could be applied to Point C to get Point D? 0 C. Determine the coordinates of Point Din terms of cosine and sine of e. D. Determine the coordinates of Point D in terms of cosine and sine of o.

9 15. The diagram below shows the unit circle. A. Determine the coordinates of Point Cin terms of cosine and sine of e. C B. Describe the relationship between Points C and D. What transformation(s) could be applied to Point C to get Point D? C. Determine the coordinates of Point Din terms of cosine and sine of e.

9 15. The diagram below shows the unit circle. A. Determine the coordinates of Point Cin terms of cosine and sine of e. C B. Describe the relationship between Points C and D. What transformation(s) could be applied to Point to get Point D? C. Determine the coordinates of Point Din terms of cosine and sine of e.

x [ 1 point Consider two concentric circles of radius 17 and 19. The larger circle has a chord, half of which lies inside the smaller circle. What is the length of the chord in the larger circle? (A) 12/2 (B) 10V3 (C) V17. 19 (D) 18 (E) 8V6 A

Rewrite the equation for this circle in Standard Form: 32 - 12x + y2 - 16y + 96 = 0 Standard Form: O=0 Center: Radius: List 4 points on the circle. . Do not use decimal approximations, • Enter radicals such as 15 as 'sqrt(15) instead of using rational exponents. • You do not need to reduce your radicals for this problem. Note: You can earn partial credit on this problem.

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