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Trigonometry

Geometrical Interpretation of tan θ

If we draw the tangent to the circle of radius 1 at the point (1,0) and extend the radial line 0P until it intersects with the tangent, we form a right angle triangle with an adjacent side of length 1.This means that the length of the opposite side must be tan θ.

Similarly for the second quadrant.  This time the extension gives a negative value for tan θ.

Exercise 8.

Where is the line segment on a unit circle representing the value of tan θ, where θ is in the 3^rd and 4^th quadrants?

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