Signs of Sines (and Other Trigonometric Ratios)Date: 07/11/2002 at 10:17:44 From: Amul Subject: Signs of trigonometric ratios Dear Dr. Math, The trigonometric ratios have the signs + or -, depending on the quadrant. How do we know it is "+" or "-" among four quadrants? Thank you. Date: 07/12/2002 at 09:17:23 From: Doctor Peterson Subject: Re: Signs of trigonometric ratios Hi, Amul. It's easy to keep track of the signs if you think about the definition of the functions in terms of a unit circle. Picture the point (x,y) moving around the unit circle; x and y change sign as you move from quadrant to quadrant, and the ratios take their signs from the combinations of these: sin cos tan quadrant x y r y/r x/r y/x -------- --- --- --- --- --- --- I + + + + + + II - + + + - - III - - + - - + IV + - + - + - You can picture it this way: cos - cos + | | tan - | tan + cos + | II|I ----------+---------- III|IV | tan + | tan - sin - | | That is, the sine is positive on the top (when y is positive), the cosine is positive on the right (when x is positive), and the tangent is positive when the sine and cosine have the same sign. This may help you, too: http://mathforum.org/library/drmath/view/53943.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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