What is the value of arcsin(3/5) & arcsin(1/sqrt5) in terms of pi radian ?

Question

With reference to Inverse Trigonometric Functions, please help me in details calculation/description for finding out the value of arcsin(3/5 & arcsin(1/sqrt5) in terms of pi radians.

Answer 1

   Set your calculator DRG / on Rad ( radian)

 

sin^-1 ( 3/ 5 ) = = 0.6 435

 

   Radians usually expressed in ratio of ∏.

 

     Sin^-1 ( 3/5 ) = (0.6435/∏ ) ∏ = 0. 2225 ∏

 

 

 Sin ^-1 ( 1/ √5 ) = (0. 4636 /∏ ) ∏ = 0. 1476 ∏

 

   These are Summary of  Steve S's   explanation.

Answer 2

pi radians = 180°, but any number can represent radians. A number of radians does not have to have pi in it. pi is just a number.

 

So arcsin(3/5) is the Quadrant I angle whose sine is 3/5. If you graph the points (0,0), (4,0), and (4,3), then connect them with line segments, you will have a 3-4-5 right triangle whose acute angle near the origin is arcsin(3/5). Arcsin(3/5) radians is the exact value for the number of radians the angle has, but you can use your calculator to get an approximate evaluation of 0.643501108793284 radians. Oh, I could divide that by pi to determine the number of pi radians there are: 0.20483276469913*pi radians, or roughly pi/5 radians.

 

arcsin(1/sqrt5) / pi = 0.14758361765043, so

arcsin(1/sqrt5) = 0.14758361765043*pi radians, or roughly 3pi/20 radians.