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MrFrizzy

  • 2 years ago

Evaluate exactly in radians: arctan(1/sqrt(3)). I know it equals tan(x)=sqrt(3)/3 and the answer is pi/6 but I do not know why. Can someone explain?

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  1. myininaya
    • 2 years ago
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    \[\arctan(\frac{1}{\sqrt{3}})=\arctan(\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}})\] The range of arctan( ) is -pi/2 to pi/2 For when do you have from -pi/2 to pi/2 that \[\tan( )=\frac{\sin( )}{\cos( )}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}\]

  2. myininaya
    • 2 years ago
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    Use unit circle.

  3. MrFrizzy
    • 2 years ago
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    Ah, your explanation is exactly what I needed to see. I never though about the fact that the sine and cosine would have common denominators and therefore cancel. Thank you

  4. myininaya
    • 2 years ago
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    np :)

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