..a little help in my review sheet for test

**ck3** · November 12th 2006, 07:43 PM

1. the degree measure of an angle Ө is 240 degree. if the arc that subtends the angle Ө has a length of 8pi, then the radius of the circle is?

2. the smallest positive solution of the equation tan4A=-2,using radian measure is?
.....i arrived an answer of 0.4636....

3. for a circle of radius 15 cm, an arc length of 36 cm corresponds to a central angle of?

......i got an answer of 1.2pi rad....

**Soroban** · November 13th 2006, 04:50 AM

Hello, ck3!

Sorry, all your answers are off . . .

1. The degree measure of an angle $\theta$ is $240^o$ .
If the arc that subtends angle $\theta$ has length $8\pi$ , find the radius of the circle.

You're expected to know this formula: . $s\:=\:r\theta$

. . where $s$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians.

We are given: . $\theta \,= \,240^o \,= \,\frac{4\pi}{3}\text{ (radians)},\:s \,= \,8\pi$

Then $s \,=\,r\theta$ becomes: . $8\pi \,=\,r\left(\frac{4\pi}{3}\right)\quad\Rightarrow\ quad\boxed{r = 6}$

2. Find the smallest positive solution of: $\tan4A \:=\:-2$ , using radian measure.

We have: . $\tan4A \,= \,-2$

Then: . $4A \:=\:\tan^{-1}(-2) \:=\:-1.107148718\quad\Rightarrow\quad A\,=\,-0.276787179$

For a positive angle, add $\pi:\;A\:=\:-0.276787179 + \pi \:\approx\:\boxed{2.865\text{ radians}}$

3. For a circle of radius 15 cm, an arc length of 36 cm corresponds to a central angle of?

We are given: . $r = 15,\:s = 36$

Then $s = r\theta$ becomes: . $36 \,= \,15\theta\quad\Rightarrow\quad \theta \,= \,\frac{36}{15} \,= \,\boxed{2.4 \text{ radians}}$

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