Question

5
0 = - in
=
in quadrant II
Given cos =
Find sin
3

Answer 1

sinΘ =
`(2)/(3)`

Explanation:

using the identity

sin²x + cos²x = 1 ( subtract cos²x from both sides )

sin²x = 1 - cos²x ( take square root of both sides )

sinx = ±
`√(1-cos^2x)`

given

cosΘ = -
`(√(5) )/(3)` , then

sinΘ = ±
`\sqrt{1-(-(√(5) )/(3))^2 }`

= ±
`\sqrt{1-(5)/(9) }`

= ±
`\sqrt{(4)/(9) }`

= ±
`(2)/(3)`

since Θ is in quadrant II where sinΘ > 0 , then

sinΘ =
`(2)/(3)`