What is the purpose, if any, of secant, cosecant, and cotangent? I’m an engineering student so I use sine, cosine, and tangent a lot, but almost never the other 3. Creating a new trig function just to be the reciprocal seems to be a bit redundant.
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All the trig functions are of the form: This is what I know, this is what I want to find out.
Most of the time, you know something about the hypotenuse of the triangle and the acute angle. The three functions you named are for when you know different things and are trying to work backwards. So for the tangent, you know the angle and get the ratio of the sides. For the cotangent you know the sides and work backwards to the angle.
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