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Usimov [2.4K]
2 years ago
13

An angle t is drawn from the center of the unit circle. Find a formula in terms of t for the straight line distance d between th

e points where the two radii meet the unit circle. Hint: By rotating the picture, you may assume that one of the radii meets the circle at the point (1,0)

Mathematics
1 answer:
Doss [256]2 years ago
5 0

Answer:

d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}

Step-by-step explanation:

Let suppose that one of the radii meets the circle at the point (1,0). The straight line distance formula is:

d = \sqrt{(\cos t - 1)^{2}+(\sin t - 1)^{2}}

d = \sqrt{(\cos^{2}t - 2\cdot \cos t + 1)+(\sin^{2}t - 2\cdot \sin t + 1)}

d = \sqrt{2-2\cdot (\cos t + \sin t )}

d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}

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Step 1: use Eq 2 to solve for x
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Step 6: Plug z in to solve for x
x=-2z+2
x= (-2)(0)+2
x= 2

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