Question

given sin(x)=6/11 and sec(x)<0 find cos(x) and tan(x)

Answer 1

\(\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies \cfrac{opposite=6}{hypotenuse=11}\)

sec(x) < 0 meaning is negative, recall that \(\bf sec(\theta)=\cfrac{hypotenuse}{adjacent}\)

if sec(x) is negative...that means the "adjcent side" is negative
because hypotenuse is just a radius and thus always positive

since the adjacent is negative
and the opposite, 6, is positive...

that means either 2nd Quadrant thus

Answer 2

so find the missing "adjacent side" and plug it in the SOH CAH TOA identities to find all 3