Question

given sin0= 2/3 and angle 0 is in quadrant 2, what is the exact value of cos0 in simplest form? simplify all radicals if needed

Answer 1

Answer: ( -
`√(5)` / 3)

Explanation:

sin(angle) = opposite/hypotenuse

opposite =2

hypotenuse = 3

solve for adjacent side with pythagorean theorum

opposite^2 + adjacent^2 = hypotenuse^2

2^2 + adjacent^2 = 3^2

4 + adjacent^2 = 9

adjacent^2 = 9 - 4

adjacent^2 = 5

adjacent =
`√(5)`

-
`√(5)` since it is in the second quadrant

cosx = (adjacent/hypotenuse)

cosx = (-
`√(5)`/3)

(-
`√(5)`/3)