If the point (3/5, 4/5) corresponds to an angle in the unit circle, what is csc x?

Solution:

Given

Point A( 3/5, 4/5)

The extremity of the arc x on the trigonometric unit circle,

tanx = y/x

= (4/5)/ (3/5)

= 4/3

x = 53°13

sinx = sin53°13

= 0.8

cscx = 1/sinx

= 1/0.8

= 1.25

Therefore, cscx = 1.25

The other way to figure this out is the coordinates of the given point (x,y) in a unit circle denotes (cosθ, sinθ)

Here 4/5 = sin θ

Csc θ= 1/ sin θ

csc θ = 5/4 

= 1.25

Therefore, cscx = 1.25

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If the point (3/5, 4/5) corresponds to an angle in the unit circle, what is csc x?

Summary:

If the point (3/5, 4/5) corresponds to an angle in the unit circle, csc x is 1.25