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CrossFit415
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Homework Statement
Why is Cosin and Secant even? Cos (-t) = cos t, Sec (-t) = sec t
Why don't they equal - sec t instead like the rest of the functions? Thanks
romsofia said:The reason why cosine is an even functions is because if you expand cosine via power series you'll get polynomials that are only even: 1-X2/2!+X4/4!-X6/6!+X8/8!...
eumyang said:I don't think this is helpful to the OP, because, unless I'm mistaken, he/she hasn't seen power series yet.
Cosine and Secant are trigonometric functions commonly used in mathematics and physics. Cosine (cos) is the ratio of the adjacent side to the hypotenuse of a right triangle, while Secant (sec) is the inverse of the cosine function.
Cosine and Secant are even functions because they exhibit symmetry about the y-axis. This means that the value of the function at any point on the positive x-axis is equal to the value at the same point on the negative x-axis.
The evenness of Cosine and Secant allows for simplification and manipulation of trigonometric equations. For example, if the variable x appears in an even power in an equation, the evenness of cosine and secant allows us to replace it with the absolute value of x.
Yes, the evenness of Cosine and Secant can be proved using the unit circle or by using the properties of even functions, such as the property that f(-x) = f(x).
Yes, there are two other trigonometric functions that are even - the Even Cosine (cosec) and Even Tangent (cot). These functions exhibit symmetry about the y-axis just like cosine and secant.