Question

How do you find the answer to this problem?

Find `sintheta if sec=4/3 and tantheta <0`

Answer 1

`sin theta = - \sqrt{1 - (3/4)^2} = - \sqrt{7}/{4}`

Explanation:

`sec theta = 4/3`

`1/cos theta = 4/3`

`cos theta = 3/4`

`cos^2 theta + sin ^2 theta = 1`

`sin theta = \pm \sqrt{1 - cos^2 theta}`

The positive cosine and negative tangent tell us the sine is negative, so we choose the negative sign.

`sin theta = - \sqrt{1 - (3/4)^2} = - \sqrt{7/16} = - \sqrt{7}/{4}`