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

1 Answer
Jul 30, 2018

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