Trigonometry (sine function)

Question

Why is the inverse of sine of (0.5/√0.5). The calculator isn't computing. I'm not getting the angle.

I thought sine = opposite/hypotenuse

x=0.5

y= 0.5

radius= √0.5

Answer 1

r² = (.5 )² + (.5)²

r²= 2 (0.5 )²

r = 0.5√2

sin θ = 0.5 / ( 0.5) √2

sinθ = 1/ √2

sinθ =√2/ 2

Then θ = sin^-1(√2/ 2)=45^° if the calculator is set on a degree mode

or θ = sin^-1(√2/ 2)=π/4 if the calculator is set in radian mode

Answer 2

inverse sine of (.5/sqr.5) = 45 degrees or pi/4

.5/sqr.5 = .5(sqr.5)/.5 = sqr.5 = about 0.707 punch .707 into your calculator then punch in inverse sine. You might get 44.999, but .707 is rounded off, and that makes the real answer of 45 look like 44.999

inverse sine of 0.707 = 45 degrees

when x=y it's 45 degrees in 1st quadrant or pi/4

but if x=y and both are negative, it's in the 3rd quadrant and angle = 180+45 = 225 degrees or 5pi/4