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April 13th, 2013, 03:01 PM  #1 
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Which line segment equals tangent of angle
The answer is the tangent from the point of tangency to the xaxis equals the tangent of the angle (got that?) Note: There is no question in here, no need to reply. I had this question on a test I just took and wanted to find out the answer. By the time I'd figured it out, I didn't want to lose all that I'd typed in here, so I leave it here for anyone's edification. [attachment=0:2zpfaohr]Capture.PNG[/attachment:2zpfaohr] The first quadrant of the unit circle is shown with a radius to point C . The angle between the radius and the xaxis is . The tangent to the circle at point C is drawn between the xaxis (point D) and yaxis (point E). The question asks which line segment is equal to the tangent of the labeled angle. The answer is the segment from the point of tangency to the xaxis (). Following is the proof The, . So we need a segment which is units long. That is, I want to show that is units long. The slope of the radius is also , so the slope of the tangent (which is perpendicular) is . Since is on the line, we can find the equation of the line: The last step uses that for any point on the unit circle. Then the xintercept of the tangent is . We need to show that the distance from to equals (don't forget that ): 
April 13th, 2013, 07:40 PM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Which line segment equals tangent of angle
Another approach would be to use right triangle OCD and tanx = opposite/adjacent Since the adjacent side equals 1 then tanx equals the length of the opposite. 
April 14th, 2013, 05:38 AM  #3  
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Re: Which line segment equals tangent of angle
Nice! Thanks. (Hopefully, your reply appears before my post when people search for this.) Quote:
 

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angle, equals, line, segment, tangent 
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