Sin or Sine is the ratio of the Opposite side Over The Hypoteneuse of any right angled triangle
inverse sin or inverse sine ( they mean the same thing ) uses the same ratio to find an unknown angle and can be written as sin-1
so if you know two sides ( opposite and Hypoteneuse ) then you can work out the sin...then you can either use a calculator to determine the inverse ( or angle ) or you could look up the sin in a booklet of sin values and determine the angle
Example : in the triangle ABC the line ab=4 ac = 5 and the angle abc =90
we could find the sin of the angle acb
sinacb= opp/hyp = 4/5 = 0.8
to find sin-1 of 0.8
calcultor press 0.8
press inv button or on newer calculators the 2nd functon button
then press the button marked sin
the display should then display 53.1301....or 53 to 2 sig figures
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1.570796327
arcsin(.75)≈0.848062079
You can calculate that on any scientific calculator. Make sure you put it into the correct angle mode (degrees, or radians, depending on what you need), and press something like "inverse", followed by "sin".In Excel, you can type: =asin(0.58333) That will give you the angle in radians.
You can use the inverse of sin when you want to solve an equation where x is the angle you're trying to find. Say sin(x)=32/50 Since you can't plug "x" into your calculator, use the arc sin (represented on your calculator by sin -1) on both sides to get rid of the sin. This is how it would plug into your calculator: sin-1 (32/50) Whatever the answer is would be what "x" equals.
Using the Sine function Sin(x) = 0.5 Then x = Sin^(-1)0.5 x = 30 degrees. Sin^(-1) in the inverse function on you calculator. . It works for Sin , Cosine and Tangent of any angle.