Question

Given sin 0 = and angle Ø is in Quadrant I, what is the exact value of cos ✪ in simplest form? Simplify all radicals if needed.

Answer 1

cosΘ =
`(√(21) )/(5)`

Explanation:

using the identity

• sin²Θ + cos²Θ = 1 ⇒ cos²Θ = 1 - sin²Θ

given Θ is in quadrant 1 , then cosΘ > 0

sinΘ =
`(2)/(5)` , then

cos²Θ = 1 - (
`(2)/(5)` )² = 1 -
`(4)/(25)` =
`(25)/(25)` -
`(4)/(25)` =
`(21)/(25)` , then

cosΘ =
`\sqrt{(21)/(25) }` =
`(√(21) )/(√(25) )` =
`(√(21) )/(5)`