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Thread: What is the direction angle of the resultant <34,-21>

  1. #1
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    What is the direction angle of the resultant <34,-21>

    How do I solve this?
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  2. #2
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    Re: What is the direction angle of the resultant <34,-21>

    The same way you solve your previous problem! You have a right triangle where one leg has length 34 and the other has (signed) length -21. Use the Pythagorean theorem to determine the length of the hypotenuse and use inverse trig functions to determine the angle.
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    Re: What is the direction angle of the resultant <34,-21>

    Quote Originally Posted by Gummg View Post
    How do I solve this?
    How does your textbook define direction angle of the resultant ?
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    Re: What is the direction angle of the resultant <34,-21>

    would it be inverse tan (21/34) or (-21/34)
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    Re: What is the direction angle of the resultant <34,-21>

    Quote Originally Posted by Gummg View Post
    would it be inverse tan (21/34) or (-21/34)
    Without knowing how the textbook defines things, it is hard to answer.
    But if $(a,b)$ is a point then the angle determined by the position vector $<a,b>$ can be found as follows.
    If $a\cdot b\ne 0$ then
    $\theta=$ $\begin{cases}\arctan\left(\dfrac{b}{a}\right) &\text{ if }a>0 \\\pi+\arctan\left(\dfrac{b}{a}\right) &\text{ if }b>0~\&~a<0 \\-\pi+\arctan\left(\dfrac{b}{a}\right) &\text{ if }a<0~\&~b<0 \end{cases}$

    So what is your answer now?
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