Question

if $p(x,y)$ is the point on the unit - circle defined by real number $\theta$, then $csc\theta=$
a. $\frac{y}{x}$
b. $\frac{1}{y}$
c. $\frac{x}{y}$
d. $\frac{1}{x}$

Explanation:

Step1: Recall trigonometric definitions on unit - circle

On the unit circle with a point $P(x,y)$ defined by the angle $\theta$, $\sin\theta=y$.

Step2: Recall the reciprocal relationship of cosecant

The cosecant function is the reciprocal of the sine function, i.e., $\csc\theta=\frac{1}{\sin\theta}$.

Step3: Substitute $\sin\theta$ value

Since $\sin\theta = y$, then $\csc\theta=\frac{1}{y}$ ($y
eq0$).

Answer:

B. $\frac{1}{y}$