Question

The point (x,sqrt7/3) in the second quadrant corresponds to angle θ on the unit circle. *blank*θ=3/sqrt of 7 *blank*θ=sqrt of 7/3 What are the blanks?

Answer 1

Answer:

csc (θ) = 3/ sqrt(7)

sin(θ)= sqrt(7)/3

Step-by-step explanation:

The point (x,sqrt7/3) in the second quadrant corresponds to angle θ on the unit circle.

The point (x,y) on the graph represents (cos theta, sin theta)

Given point is $(x,\frac{\sqrt{7} }{3} )$

cos(θ) =x

sin(θ)= sqrt(7)/3

csc (θ) is the inverse of sin(θ)

So csc (θ) = 3/ sqrt(7)

Answer 2

Since the point lies on the unit circle, its distance from the origin is 1.

So,

$\sin\theta=\dfrac{\frac{\sqrt7}3}1=\dfrac{\sqrt7}3$

which means

$\csc\theta=\dfrac1{\sin\theta}=\dfrac3{\sqrt7}$