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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 ):

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April 13th, 2013, 07:40 PM   #2
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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.

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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.

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