Question

How do you use `csctheta=4` to find `costheta`?

Answer 1

`cos theta=0.968245836`

Explanation:

`cosec theta=4`

the opposite of `cosec theta= sin theta`

`sin theta= 0.25`

`theta =14°.47751219`

`= 14°28'39"`

`theta` lies in the first quadrant where sin and cos= +

`cos theta = 0.968245836`

Answer 2

Use the identities `csc(theta) = 1/sin(theta) and cos(theta) = +-sqrt(1 - sin^2(theta)`

Explanation:

Given: `csc(theta) = 4` Find `cos(theta)`

Use the identity `csc(theta) = 1/sin(theta)`:

`1/sin(theta) = 4`

`sin(theta) = 1/4`

Substitute `(1/4)^2` for `sin^2(theta)` into the identity: `cos(theta) = +-sqrt(1 - sin^2(theta)`:

`cos(theta) = +-sqrt(1 - (1/4)^2)`

`cos(theta) = +-sqrt(1 - 1/16)`

`cos(theta) = +-sqrt(15/16)`

`cos(theta) = +-sqrt(15)/4`

Because we are not given any clue to whether `theta` is in the first or second quadrant, we cannot determine whether the cosine is positive or negative.