# Thread: ..a little help in my review sheet for test

1. ## ..a little help in my review sheet for test

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?

2. Hello, ck3!

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

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

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

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

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

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

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

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

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

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

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

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