Question

If cosine theta equals two over three, what are the values of sin θ and tan θ?

Answer 1

see explanation

Explanation:

Using the identity

sin²x + cos²x = 1 then

sin²x = 1 - cos²x

sin x = ±
`√(1-cos^2x)`

Given cos θ =
`(2)/(3)` , then

sinθ = ±
`\sqrt{1-((2)/(3))^2 }` = ±
`\sqrt{1-(4)/(9) }` = ±
`\sqrt{(5)/(9) }` = ±
`(√(5) )/(3)`

Also

tanθ =
`(sin0)/(cos0)`

=
`((√(5) )/(3) )/((2)/(3) )`

=
`(√(5) )/(3)` ×
`(3)/(2)` = ±
`(√(5) )/(2)`

Answer 2

what

Explanation: