In many cases we will want to know the reciprocal ratios of
trigonometric functions. The reciprocal is found by turning the
fraction upside down.
So the reciprocal of the sine function is called the cosecant and
is equal to the hypotenuse / opposite. The reciprocal of the cosine
function is called the secant and is equal to the hypotenuse /
adjacent, and the reciprocal of the tangent function is called the
cotangent and is equal to the adjacent / opposite.
It is important to note that there is a big difference between
the reciprocal value csc θ and sin-1x. The cosecant
function means 1/sin θ, while the second involves finding an angle
whose sine is x.
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