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April 13th, 2013, 03:01 PM   #1
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Which line segment equals tangent of angle

The answer is the tangent from the point of tangency to the x-axis 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 x-axis is . The tangent to the circle at point C is drawn between the x-axis (point D) and y-axis (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 x-axis (). 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 x-intercept of the tangent is .

We need to show that the distance from to equals (don't forget that ):

Attached Images Capture.PNG (11.1 KB, 117 views) April 13th, 2013, 07:40 PM #2 Math Team   Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 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
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Re: Which line segment equals tangent of angle

Nice! Thanks. (Hopefully, your reply appears before my post when people search for this.)
Quote:
 Originally Posted by agentredlum 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.  Tags angle, equals, line, segment, tangent Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tom33 Algebra 8 February 16th, 2014 03:46 PM yogazen2013 Algebra 1 August 24th, 2013 02:30 PM talisman Algebra 3 August 27th, 2012 01:48 AM Marwa Shams Algebra 1 May 7th, 2011 10:25 AM honzik Applied Math 1 June 10th, 2009 05:20 PM

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