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Math Help - ..a little help in my review sheet for test

  1. #1
    ck3
    ck3 is offline
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    ..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?

    ......i got an answer of 1.2pi rad....
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  2. #2
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    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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