The point (-3, 3) lies on the terminal side of an angle in standard position. Find the value of theta in degrees.

Question

Anybody know how to solve it and what's the answer?

Answer 1

r=√(x^2+y^2) is the distance from (0,0) to (x,y) or (-3,3)

cosθ=x/r and sinθ=y/r

r=√(9+9)=√18=3√2

cosθ=-3/3√2=-1/√2=-√2/2

sinθ=3/3√2=1/√2=√2/2

(cosθ,sinθ)=(-√2/2,√2/2)

look on the unit circle

these coordinates are at 3∏/4=135º

θ=135º

Answer 2

Graphing the point places it in the 2nd quadrant. Thus, the angle falls between 90° and 180°.

tan α = opposite side/adjacent side = 3/-3 = -1

α = tan^-1 (-1)

α =135°