Question

Find sin θ if cos θ = 4/7 and θ in quadrant IV.

Answer 1

sinΘ = -
`(√(33) )/(7)`

Explanation:

Using the trigonometric identity

sin²Θ + cos²Θ = 1, thus

sinΘ = ±
`√(1-cos^20)`

Since Θ is in the fourth quadrant then sinΘ < 0

Given

cosΘ =
`(4)/(7)` , then

sinΘ = -
`\sqrt{1-((4)/(7))^2 }` = -
`\sqrt{1-(16)/(49) }` = -
`\sqrt{(33)/(49) }` = -
`(√(33) )/(7)`