Understanding the csc (cosecant) function and how to find its values through sine ratios

Csc y values

The csc (cosecant) function is the reciprocal of the sine function

The csc (cosecant) function is the reciprocal of the sine function. It is defined as csc(y) = 1 / sin(y), where y is an angle in radians.

To find the values of csc(y), you need to determine the corresponding values of sin(y) and then take their reciprocal.

Here is a brief overview of the sine values for some common angles:

– For y = 0 degrees or 0 radians, sin(y) = 0. Therefore, csc(y) is undefined since division by zero is not possible.

– For y = 30 degrees or π/6 radians, sin(y) = 1/2. Therefore, csc(y) = 1 / (1/2) = 2.

– For y = 45 degrees or π/4 radians, sin(y) = √2/2. Therefore, csc(y) = 1 / (√2/2) = √2.

– For y = 60 degrees or π/3 radians, sin(y) = √3/2. Therefore, csc(y) = 1 / (√3/2) = 2/√3.

– For y = 90 degrees or π/2 radians, sin(y) = 1. Therefore, csc(y) = 1 / 1 = 1.

– For y = 180 degrees or π radians, sin(y) = 0. Therefore, csc(y) is undefined since division by zero is not possible.

These are just a few examples, but you can follow the same process to find the csc(y) values for any other angle. Remember to find the value of sin(y) first and then take its reciprocal to determine csc(y).

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