The points on a unit circle are the points (x,y) such that:
[tex]x^2+y^2=1[/tex]
Where x and y are real numbers.
The following illustrates the unit circle:
The point P(x,y) is shown on the unit circle.
Notice that a right triangle with legs of lengths x and y and hypotenuse of length 1 (signifies the radius).
Recall the trigonometry ratio:
[tex]\csc \theta=\frac{\text{Hypotenuse}}{\text{opposite}}[/tex]
Substitute the length of the opposite side (y) and the length of the hypotenuse (1) into the ratio:
[tex]\Rightarrow\csc \theta=\frac{1}{y}[/tex]
Hence, the correct answer is option C.
