Find tan(x) and sin(x), given sec(x)=4 and sin(x)<0

Question

I have a few more problems like this one. I'm in 12th grade pre-calculus at my school and I need to do corrections on a could things so I can graduate! I could really use some help!

Answer 1

Hi Tori,

sec(x) = 4, we know that sec(x) = 1/cos(x)

cos(x)=1/4

We know that cos(x) = adj/hyp , so  adj = 1 and hyp = 4, we need to find opp because   sin(x) = opp/hyp 

hyp² = opp² + adj²

  4²  = opp² + 1²

   16 = opp² +1 

   15 = opp²  so that opp =±√15. Not that sin (x)<0 so you chose the value of opp with the negative sign

 

sin(x) = - √15 /4 and tan(x) =sin(x)/cos(x) =(- √15 /4)/(1/4)=(- √15 /4)/(4/1)=- √15 

tan(x)= - √15