Find the exact value of sin(θ) if θ is in standard position and the terminal side of θ is in Quadrant III and is parallel to the line 7y − 2x + 6 = 0.

Answer 1

slope of the given line = 2/7
then tanθ = 2/7 = y/x ---> x = 7, y = 2 or in III x = -7, y = -2
in your right-angled triangle,
r^2 = 49+4 = 53
r = √53

sinθ = -2/√53