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Math Help - Unit circle and right angle problem?

  1. #1
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    Unit circle and right angle problem?

    if cot(-180 degrees)
    would you add 360 to get positive 180
    then do cot (180) to get 1/0 or undefined

    my second problem is if tan= 1.3
    what is the value of (cot-angle)
    I am not sure how to do this.

    Can anyone help me please?
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  2. #2
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    Also I am trying to find the tan of 150 degrees
    so I have to dive (1/2)/(- square root 3/2) can anyone also show me how to do this.
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  3. #3
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    Quote Originally Posted by homeylova223 View Post
    if cot(-180 degrees)
    would you add 360 to get positive 180
    then do cot (180) to get 1/0 or undefined

    my second problem is if tan= 1.3
    what is the value of (cot-angle)
    I am not sure how to do this.

    Can anyone help me please?
    A clockwise movement of 180^o brings us to the same position on the unit-circle

    as a counterclockwise rotation of 180^o

    sin\left[180^o\right]=sin\left[-180^o\right];\;\;\;cos\left[180^o\right]=cos\left[-180^o\right]

    Hence cot\left[180^o\right]=cot\left[-180^o\right]

    \displaystyle\ cotx=\frac{1}{tanx}=\frac{cosx}{sinx}


    For x=-180^o, sin\left[-180^o\right]=0

    hence the cotangent of that angle is undefined.


    \displaystyle\ tan\theta=1.3\Rightarrow\ cot\theta=\frac{1}{tan\theta}=\frac{1}{1.3}

    For cotangent, you only need know that it is the reciprocal of tangent.

    150^o=180^o-30^o

    \displaystyle\ tan\left[150^o\right]=\frac{sin\left[150^o}{cos\left[150^o\right]}

    In the unit-circle, sin\theta=sin\left[180^o-\theta\right]

    and cos\theta=-cos\left[180^o-\theta\right]

    Therefore

    \displaystyle\frac{sin\left[150^o\right]}{cos\left[150^o\right]}=\frac{sin\left[30^o\right]}{-cos\left[30^o\right]}

    =\displaystyle\frac{\left(\frac{1}{2}\right)}{-\left(\frac{\sqrt{3}}{2}\right)}=\frac{\left(\frac  {1}{2}\right)}{\left(\frac{1}{2}\right)}\;\left[-\frac{1}{\sqrt{3}}\right]
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