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They are usually introduced in mathematics as trigonometric ratios.
In a right angled triangle, there is (by definition) a right angle and the side opposite that is called the hypotenuse. Select one of the two acute angles, X. It is formed by two sides, one of which is the hypotenuse and the other is called the adjacent side. The third side, opposite the selected angle, is called the opposite side.
Suppose the lengths of these three sides are h, a and o. Then
sin(X) = o/h cosec(X) = 1/sin(X) = h/o
cos(X) = a/h sec(X) = 1/cos(X) = h/a
tan(X) = o/a cot(X) = 1/tan(X) = a/o
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In trig how is the value of r interpreted geometrically in the definitions of the sine cosine secant and cosecant?
In trigonometry, the value of R is the radius of the circle, and is usually normalized to a value of 1. If the circle is at the X-Y origin, and theta is the angle between the radius line R, and X and Y are the X and Y coordinates of the point on the circle at the radius line, then... sine(theta) = Y / R cosine(theta) = X / R secant(theta) = 1 / cosine(theta) = R / X cosecant(theta) = 1 / sine(theta) = R / Y
When is secant not defined?
The secant of an angle is the reciprocal of the cosine of the angle. So the secant is not defined whenever the cosine is zero That is, whenever the angle is a multiple of 180 degrees (or pi radians).
What is the difference between a tangent and a secant?
They are different trigonometric ratios!
What is the secant of 90 degrees?
The secant function is not defined for odd multipls of 90o.
When does a secant of a circle pass through the center of the circle?
The secant of a circle passes through the center of a circle sometimes
