To find sin a when we know that cos a = -2/3, we can use the Pythagorean identity:
sin^2(a) + cos^2(a) = 1
From the given information, we have:
(-2/3)^2 + sin^2(a) = 14/9 + sin^2(a) = 1sin^2(a) = 1 - 4/9sin^2(a) = 5/9
Taking the square root of both sides, we get:
sin(a) = ±√(5/9)sin(a) = ±√5/3
Therefore, sin a = ±√5/3.
To find sin a when we know that cos a = -2/3, we can use the Pythagorean identity:
sin^2(a) + cos^2(a) = 1
From the given information, we have:
(-2/3)^2 + sin^2(a) = 1
4/9 + sin^2(a) = 1
sin^2(a) = 1 - 4/9
sin^2(a) = 5/9
Taking the square root of both sides, we get:
sin(a) = ±√(5/9)
sin(a) = ±√5/3
Therefore, sin a = ±√5/3.