Question

Question #b6bb2

Answer 1

`costheta=-3/5`

Explanation:

Given
`sintheta = 4/5`
`4/5>0`
`sin theta` is not in first quadrant
where `costheta` is positive
we know that
`sintheta>0` both in first and second quadrants
`But costheta` is negative in second quadrant
`5` being hypotnuse
`4` being opposite side
the adjacentside can be evaluated by pythagoras theorem
adjacent side is `sqrt((5^2-4^2))`=`3`
Now
`3` being adjacent side
`5` being hypotenuse`costheta=3/5`
In second quadrant, being negative,
`costheta=-3/5`

Answer 2

`costheta=-3/5`

Explanation:

`"using the "color(blue)"trigonometric identity"`

`•color(white)(x)sin^2theta+cos^2theta=1`

`rArrcostheta=+-sqrt(1-sin^2theta)`

`"since "sintheta>0" and not in first quadrant then"`

`theta" must be in the second quadrant where "costheta<0`

`rArrcostheta=-sqrt(1-(4/5)^2)`

`color(white)(rArrcostheta)=-sqrt(9/25)=-3/5`