- Thread starter
- #1
karush
Well-known member
- Jan 31, 2012
- 3,252
In the figure, the length of the chord $AB$ is $4 \text { cm}$ and the length of the arc is $5\text{ cm}$
View attachment 1713
(a) Find the central angle $\theta$, in radians, correct to four decimal places.
(b) Give the answer to the nearest degree
this problem is intended to be solved by Newton's Method, so I am have ?? as to how to set it up. I thot that using law of cosines would be part of it since
$$\cos{\theta} = \frac{4^2}{a^2+b^2-2ab}$$
or since $a=b=r$
$$\cos{\theta} = \frac{16}{2r^2-1}$$
and
$$\cos^{-1}{\left(\frac{16}{2r^2-1}\right)}=\theta$$
and also $$S=\theta\cdot r$$ for arc length
so this is where I have a flat tire without a spare....
View attachment 1713
(a) Find the central angle $\theta$, in radians, correct to four decimal places.
(b) Give the answer to the nearest degree
this problem is intended to be solved by Newton's Method, so I am have ?? as to how to set it up. I thot that using law of cosines would be part of it since
$$\cos{\theta} = \frac{4^2}{a^2+b^2-2ab}$$
or since $a=b=r$
$$\cos{\theta} = \frac{16}{2r^2-1}$$
and
$$\cos^{-1}{\left(\frac{16}{2r^2-1}\right)}=\theta$$
and also $$S=\theta\cdot r$$ for arc length
so this is where I have a flat tire without a spare....
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