csc(s)=1.4148624?

Question

This is probably easy but I can't find it in the book anywhere. Can someone please help. Thanks

Answer 1

Because this is done with a decimal that may not be exact, I'm going to find the value of s in degrees. We know that cosecant is the reciprocal or sine, so...

csc(s) = 1.4148624
==> take reciprocals
1 / csc(s) = 1 / 1.4148624
==> simplify each side
sin(s) = 0.706782511
==> take the inverse sine
arcsin(sin(s)) = arcsin(0.706782511)
==> left side cancels to "s," calculator for right side
s = 44.97°

To find the value in radians, multiply by (π/180°):

(44.97°)*(π / 180°) = 0.784939681

We see that this is about 45 degrees, so it's possible that your value is meant to be π/4 in radians but you lost precision because you have a decimal that cuts off.

Answer 2

First, find a definition of a cosecant. Try Google if your book really doesn't have it.
Next, convert to a more familiar and easy to find function.
Last, look up the arc value of the more familiar function.
Yes, I know the answer, and no, I won't tell you what it is.

Answer 3

csc is the reciprocal of sin

1.414=sqrt2

csc(s)=sqrt2 means sin(s)=(sqrt2)/2

using the unit circle, sin is positive in quadrants I and II, which would be 45 and 135 degrees or pi/4 and 3pi/4 in radians

Answer 4

Let cosec θ = 1.4148624
1 / sin θ = 1.4148624
sin θ = 1 / 1.4148624
θ = 45° , 135°

Answer 5

sin(s)= 1/1.4148624=0.7068
s=44.97degreesANS