Question

Is the point on the unit circle defined by real numbers

Answer 1

The points on a unit circle are the points (x,y) such that:

`x^2+y^2=1`

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:

`\csc \theta=\frac{\text{Hypotenuse}}{\text{opposite}}`

Substitute the length of the opposite side (y) and the length of the hypotenuse (1) into the ratio:

`\Rightarrow\csc \theta=(1)/(y)`

Hence, the correct answer is option C.