SOLUTION: Find exact value of Trigonometry functions using the Unit Circle. tan(pie/3). I know it's square root 3 but how?

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Question 215393: Find exact value of Trigonometry functions using the Unit Circle.
tan(pie/3). I know it's square root 3 but how?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

From the unit circle, for , and , so

John

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find exact value of Trigonometry functions using the Unit Circle.
tan(pie/3). I know it's square root 3 but how?
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Draw a unit-circle (radius = 1)
Sketch a 60 degree angle in the 1st quadrant with one side on the +x-axis.
Comment: The other side of the angle will meet the circle at P(x,y).
Sketch a line segment from P perpendicular to the +x-axis.
Comment: You now have a right triangle.
The hypotenuse is "1" because the radius is "1".
The angle at P is 30 degrees.
The side opposite that angle is 1/2 the hypotenuse of (1/2).
The side opposite the 60 degree angle is "y".
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Using Pythagoras
y^2 = 1^2-(1/2)^2
y^2 = 3/4
y = sqrt(3)/2
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So, the tan(pi/6) = y/(1/2) = [sqrt(3)/2)/(1/2) = sqrt(3)
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Cheers,
Stan H.