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

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

So,


`\sin\theta=\frac{\frac{\sqrt7}3}1=\frac{\sqrt7}3`

which means


`\csc\theta=\frac1{\sin\theta}=\frac3{\sqrt7}`

Answer 2

csc (θ) = 3/ sqrt(7)

sin(θ)= sqrt(7)/3

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,(√(7) )/(3) )`

cos(θ) =x

sin(θ)= sqrt(7)/3

csc (θ) is the inverse of sin(θ)

So csc (θ) = 3/ sqrt(7)