Question

Find the exact value of sin 0 if cos 0=-2/3 and 90º < 0 < 180°

Answer 1

sin (theta) =
`(√(5) )/(3)`

Explanation:

cos = adjacent side/hypotenuse

Then, in a right triangle the adjacent = 2 and the hypotenuse = 3

By the Pythagorean theorem, 3^2 = 2^2 + opposite side^2

9 - 4 = 5

opposite side =
`√(5)\\`

sin (theta) =
`(√(5) )/(3)`

An easier way is to find sin(arccos (-2/3) =
`(√(5) )/(3)`

Note: Remember that the sin is positive in the 2nd quadrant.