Date: 9/29/96 at 16:19:20 From: Ron Turner Subject: Help Dr. Math, I am having a real problem knowing when to use sine, cosine, and tangent. I am taking geometry by home study and don't quite understand. Thanks! Shauna
Date: 10/29/96 at 20:16:16 From: Doctor Lynn Subject: Re: Help Shauna, The first thing to remember is that sine and cosine are opposites, but tangent is different because it doesn't use the hypotenuse. In a triangle that looks something like the following, the three definitions are: sin x = Opposite/Hypotenuse cos x = Adjacent/Hypotenuse tan x = Opposite/Adjacent /| / | / | / | / | / | H / | / | O / | / | / | Some people like to remember the rules like this: / | / \ | O A O / x \ | ----- ----- ----- (Soh-Cah-Toa) /--------------| S * H C * H T * A A To use the triangles of letters, you cover up what you want to find. So to find the formula for sine, you cover up the S in the first triangle and you're left with O/H = opposite/hypotenuse. To find a formula for the hypotenuse, you cover the H in either the first or the second triangle and you're left with either O/S = opposite/sine or A/C = adjacent/cosine. As an example, say you want to find the height of this triangle: /| / | 10 m / | / | / | / | / 30\ | /--------------| This means that you are trying to find the length of the side which is opposite the 30 degree angle, so you could use either sine or tangent. You only know the length of the hypotenuse (10 m), however, so you can't use the tangent. So you use the first triangle of letters: O ----- S * H When you cover up the O (what you want to find), this becomes: S * H The opposite side = Sine * Hypotenuse = sin 30 * 10m = 0.5 * 10m = 5m. So the triangle is 5m high. If you remembered the three definitions, you could have used those too: sine = opposite/hypotenuse sin 30 = opposite/10 opposite = 10*sin 30 = 10*0.5 = 5m One more point - you can remember the letter triangles with this mnemonic: Silly Old Hag Cracks All Her Teeth On Apples. S = O / H, C = A / H, T = O/ A The only way to get really good at trigonometry is practice :) I hope that helps. Please write back if you have any more problems. -Doctor Lynn, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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