Attachment 23030

What is the method of calculating arc length in In the image above .

x & y is known

Thanks .

Feuilleton :

Obviously, the use of calculators and trigonometric tables is not allowed

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- Dec 7th 2011, 05:58 AMsubuntuHow to calculate arc length in unit circle
Attachment 23030

What is the method of calculating arc length in In the image above .

x & y is known

Thanks .

Feuilleton :

Obviously, the use of calculators and trigonometric tables is not allowed - Dec 7th 2011, 06:05 AMQuackyRe: How to calculate arc length in unit circle
Can we not just use the fact that $\displaystyle \tan\theta=\frac{y}{x}$?

- Dec 7th 2011, 06:06 AMcorsicaRe: How to calculate arc length in unit circle
Recognize that the arc length is the same as the angle between line $\displaystyle r$ and line $\displaystyle x$.

Lines $\displaystyle r$, $\displaystyle x$ and $\displaystyle y$ form a right triangle. Thus you can use the formula:

$\displaystyle \tan(\theta)=\frac{y}{x}$ - Dec 7th 2011, 06:46 AMPlatoRe: How to calculate arc length in unit circle
Does the question ask for the arc-length from $\displaystyle (1,0)$ to $\displaystyle (x,y)$ in the

**first quadrant**.

If so the answer is $\displaystyle \arccos \left( {\frac{x}{{\sqrt {x^2 + y^2 } }}} \right)$.

That is the measure of the central angle times the radius which in this case is $\displaystyle R=1$.

If it could be that $\displaystyle (x,y)\in II$ the same formula works.

Now if $\displaystyle (x,y)\in III\text{ or }IV$ then we need to know if we are still measuring in a counter-clockwise direction or not.

This directiveis impossible to follow except for a very, very few values of $\displaystyle x~\&~y$.*the use of calculators and trigonometric tables is not allowed* - Dec 7th 2011, 01:55 PMProve ItRe: How to calculate arc length in unit circle
- Dec 7th 2011, 02:14 PMPlatoRe: How to calculate arc length in unit circle
- Dec 7th 2011, 02:16 PMProve ItRe: How to calculate arc length in unit circle