The function, denoted as , is the inverse of the sine function. While sine takes an angle and gives a ratio, arcsine takes a ratio and returns the original angle. 1. Define the Domain and Range
, you are asking: "What arc length (angle) gives me this vertical height?"
. It is an increasing function that passes through the origin 4. Apply Calculus Properties arcsine
is a reflection of the restricted sine curve across the line
π2the fraction with numerator pi and denominator 2 end-fraction 3. Visualize the Function The graph of The function, denoted as , is the inverse
π6the fraction with numerator pi and denominator 6 end-fraction
: Calculating the angle of refraction using Snell's Law. arcsine
−π2negative the fraction with numerator pi and denominator 2 end-fraction