Question

Find the exact value of all six trigonometric functions if `sin theta =8/17` and `cos theta < 0`?

Answer 1

See explanation...

Explanation:

Given that `sin theta = 8/17` and `cos theta < 0`, we have:

`cos theta = -sqrt(1-sin^2 theta)`

`color(white)(cos theta) = -sqrt(1-(color(blue)(8/17))^2)`

`color(white)(cos theta) = -sqrt(1-64/289)`

`color(white)(cos theta) = -sqrt(225/289)`

`color(white)(cos theta) = -15/17`

Then:

`tan theta = sin theta / cos theta = -8/15`

`cot theta = cos theta / sin theta = -15/8`

`sec theta = 1 / cos theta = -17/15`

`csc theta = 1 / sin theta = 17/8`