An angle 𝛼 in standard position has a terminal side which passes through the point (−5,5). What is sin( 𝛼)

Question

I got to five square root of two but I am not sure how to proceed after that.

Answer 1

The angle α is shown in the sketch but we can use the reference angle (β) to find the sin(α) because sin(β) = sin(α).

The hypotenuse is √[(5)² + (-5)^√2] = √(25 + 25) = √50 = 5√2

sin(β) = opp/hyp = 5/(5√2) = 1/√2 and then we rationalize this by multiplying by √2/√2 to get sin(β) = √2/2

So since sin(α) = sin(β) then sin(α) = √2/2