Respuesta :

When an angle lies along an axis, the values of the trigonometric functions are either 0, 1, -1, or undefined. When the value of a trigonometric function is undefined, it means that the ratio for that given function involved division by zero.

When the angle θ is nπ where n=0,1,2,3….. i.e. the angle lies on x-axis, the value of csc θ is undefined.

What is csc θ?

csc θ is bascically cosecθ  which is the reciprocal of sinθ

cosecθ= 1/sinθ

csc θ will be undefined when denominator is 0 i.e. sinθ  is 0.

The value of sinθ is 0, when θ will be 0,π,2π,3π....... i.e. θ=nπ where n=0,1,2,3,.......

Therefore when the angle θ is nπ where n=0,1,2,3….. i.e. the angle lies on x-axis, the value of csc θ is undefined.

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