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Math Help - Equivalent expression for sin(-7pi/6) in terms of the related acute angle.

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    Equivalent expression for sin(-7pi/6) in terms of the related acute angle.

    State an equivalent expression for sin (-7pi/6) in terms of the related acute angle.

    I don't really know how to solve these kind of questions, I find everything I google doesn't explain how to do it
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  2. #2
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    Quote Originally Posted by kmjt View Post
    State an equivalent expression for sin (-7pi/6) in terms of the related acute angle.

    I don't really know how to solve these kind of questions, I find everything I google doesn't explain how to do it
    HI

    Put it in degrees so that its easier for you to see.

    \sin (-\frac{7\pi}{6})=\sin (-210)=-\sin 210=\sin 30=0.5

    Note that \sin 30=\sin 150=-\sin 210=-sin 330
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    I'm not following =/ I know that sin (-7pi/6) is the same thing as sin (-210 degrees) but i'm not sure where to go from there. I'm not even sure what the question is asking
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    Quote Originally Posted by kmjt View Post
    I'm not following =/ I know that sin (-7pi/6) is the same thing as sin (-210 degrees) but i'm not sure where to go from there. I'm not even sure what the question is asking
    OK , try to follow here . I will go slow .

    \sin (-210)=-\sin 210 (Step 1)

    -\sin 210=-(-\sin 30) (Step 2)

    This is because sin is negative in the 3rd quadrant .

    -(-\sin 30)=\sin 30 (Step 3)

    I think this is what the question wants since it asks for acute angles (angle < than 90 degree)

    If you still have any problem , just indicate which step you are unsure with .. don say everything or else i don know where to start .
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    Where is the-(-sin30) coming from?
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    Quote Originally Posted by kmjt View Post
    Where is the-(-sin30) coming from?
    sin 210 = - sin 30

    - sin 210 = - ( - sin 30 )
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    It just clicked in my brain thanks!
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  8. #8
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    I don't see why degrees should be easier than radians and I think it is good to encourage people to think in terms of radians. \frac{7\pi}{6}= \pi+ \frac{\pi}{6}. Since the angle is negative, we swing down from the positive x axis to the negative y axis and then [itex]\pi/6[/itex] above. Now we are in the second quadrant where sine is still postive.

    sin(-\frac{7\pi}{6})= sin(\frac{\pi}{6}).
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