If possible, find an approximate solution to sin(𝜃)=1/4

Question

Just confused on how to approximate this in radians

Answer 1

use a calculator with an inverse trig function

or go on line to desmos which has an on line calculator with an inverse sine function

sinx = 1/4

x = 14.478 degrees, approximately

or 180-14.478 = 165.522 degrees

or 14.478 + 360n where n = any integer

or 165.522 + 360n where n = any integer

or x=14.478 times pi/180 = 14.478pi/180 = about 0.08pi radians = about 0.2527 radians + 2npi radians where n= any integer

or 165.522 times pi/180 = 0.9196pi radians = 2.889 radians + 2npi radians where n= any integer

sinx=1/4 has an angle in the 1st or 2nd quadrant, where x could be an infinite number of different values, positive or negative

Answer 2

sin(theta)=1/4

sin^(-1)(sin(theta))= sin^(-1)(1/4)

sin^(-1)(1/4)= 0.2526 rads. or 14.47 degrees