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Math Help - degrees / radians

  1. #1
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    degrees / radians

    Ok, I have some questions, these are all using radians

    Question 1
    Convert the following angles to radians giving your answers correct to 3SF.
    a) 20 degrees
    b) -72 degrees
    c) 400 degrees
    d) -140 degrees
    e) 760 degrees

    Question 2
    An angle "p" subtends an arc of length 25cm in a circle of radius R cm.
    The area of the sector POQ is 72cm (squared)
    Forumulate two equations in r and "p" Find the values of r and "p"

    Question 3
    A cylindrical pipe of diameter 1.5m contains water to a depth of 0.9m.
    a) find the cross sectional area of the water
    b) if the water is flowing at a rate of 60 litres per second fin dthe speed of the water in m/s


    I would really appreciate any help offered, these are the final pieces of some homework and i really need help, thank you
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Kim2425 View Post
    Question 1
    Convert the following angles to radians giving your answers correct to 3SF.
    a) 20 degrees
    b) -72 degrees
    c) 400 degrees
    d) -140 degrees
    e) 760 degrees
    The relationship between degrees and radians is that \pi rad = 180 degrees.

    a) \frac{20 \, degrees}{1} \cdot \frac{\pi \, rad}{180 \, degrees} \approx 0.349 \, rad

    The others are done the same way.

    -Dan
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  3. #3
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    Hello, Kim!

    You're expected to know these formulas.

    In a circle of radius r with a central angle of \theta radians:

    . . the length of arc is: . s \:=\:r\theta

    . . the area of the sector is: . A \:=\:\frac{1}{2}r^2\theta


    2) An angle \theta subtends an arc of length 25cm in a circle of radius R cm.
    The area of the sector POQ is 72 cm².
    (a) Formulate two equations in R and \theta.
    (b) Find the values of R and \theta.

    Part (a)

    We know that the arc length is 25 cm.
    . . So we have: . R\theta\:=\:25 [1]

    We know that the area of the sector is 72 cm².
    . . So we have: . \frac{1}{2}R^2\theta\:=\:72 [2]


    Part (b)

    Divide [2] by [1]: . \frac{\frac{1}{2}R^2\theta}{R\theta} \:=\:\frac{72}{25}\quad\Rightarrow\quad\boxed{R \,=\,\frac{144}{25}\text{ cm}}

    Substitute into [1]: . \frac{144}{25}\theta\:=\:25\quad\Rightarrow\quad\b  oxed{\theta \,=\,\frac{625}{144}\text{ radians}}

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