Question

If sin⁡ θ=−4/5, and 270° < θ < 360°what is cos θ?

Answer 1

cosΘ =
`(3)/(5)`

Explanation:

Using the trigonometric identity

sin² x + cos²x = 1

⇒ cosx = ±
`√(1-sin^2x)`

Since 270 < Θ < 360 then cosΘ > 0

cosΘ =
`√(1-(4/5)^2)`

=
`\sqrt{1-(16)/(25) }`

=
`\sqrt{(9)/(25) }` =
`(3)/(5)`

Answer 2

Here is your answer


`[I am using ☆ instead of theta]`


`sin☆= -4/5`


`{sin}^(2)☆= {(-4/5)}^(2)= 16/25`

Now,


`cos☆= \sqrt{1-{sin}^(2)☆}`


`cos☆= √(1- (16/25))`


`cos☆= √((25-16)/25)`


`cos☆= √(9/25)`


`cos☆= 3/5`

HOPE IT IS USEFUL