what if you're given something like sec = square root of 3 and tan <0

Question

so m problem here is that i know sec is equal to r/x so to me it seems like r= square root of 3

but then that makes x = 1 but then theres no possible value for y that wouldnt be a fraction. i know this bec r=square root of x^2+y^2

please help, thank you

Answer 1

It's the ratio that counts. It doesn't matter if r = 10√3 because x will be 10 and the ratio is 10√3/10 = √3. So use the simplest values of r and x, r = √3 and x = 1 and y = √(r²-x²) = √(3-1) = ±√2 (which is an irrational number, so it cannot be represented as a fraction).

If tan θ < 0, then θ is in quadrant II or IV. If sec θ > 0, then we're down to quadrant IV so y = -√2.