TangentDate: 02/14/2003 at 10:10:10 From: Laura Subject: Trigonometry Is the trigonometric ratio tangent related to the tangent of a circle? Date: 02/14/2003 at 10:21:20 From: Doctor Jerry Subject: Re: Trigonometry Hi Laura, Yes. Draw a coordinate axis - just as when you sketch an (x,y)-plane. Draw a unit circle, centered at the origin. Draw a tangent to this circle, upward from B=(1,0). Draw a line L from (0,0) to this tangent line - do this so that L is in the first quadrant. Let A be the point where L meets the tangent line. The line L makes an angle theta with the x-axis. Note that tan(theta) = AB/1 = AB. - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ Date: 02/17/2003 at 10:44:27 From: Laura Subject: Trigonometry Having read about the relation between the tangent of a circle and the tan ratio used in trigonometry, I wondered if the sine and cosine ratios were also linked to circles? If so, what about cotangent, secant and cosecant? Date: 02/17/2003 at 12:10:04 From: Doctor Jerry Subject: Re: Trigonometry Hi Laura, Yes, one can show that sine and cosine have natural interpretations (see below); maybe one could give interpretations for cotangent, secant, and cosecant (each of this is the reciprocal of sine, cosine, or tangent), but I believe the interpretations would be somewhat artificial and not terribly useful. For sine and cosine, draw a coordinate axis, just as when you sketch an (x,y)-plane. Draw a unit circle, centered at the origin. Draw a line L from (0,0) to the unit circle. It can be in any quadrant. Let theta be the angle needed to rotate the positive x-axis counterclockwise until it conincides with L. Let A=(a,b) be the point where L intersects the unit circle. It is quite easy to see that a = cos(theta) and b = sin(theta). - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ Date: 02/17/2003 at 13:58:34 From: Laura Subject: Thank you (Trigonometry) Thank you very much for your help in answering my questions. Maths is my favourite subject and I quite often drive my teacher up the wall with all my "but why?"'s. I have been able to follow your instructions and prove how it works for myself. I will show my teacher this week. Thank you. |
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