if sin x = -1/3 find the possible values of (a) sec x

Question

what is the value of sec x ?

Answer 1

-1/3=-0.333333333333333

invers sine giv -19.47122063419064 deg

?? sekant ??..=1/kosine

kosine(-19.47122063419064...)=0.942809041583809

for all trig stuff, yu kan add or subtrakt 360n tu get same anser

kosine be symmetrik...kosine(x)=kosine(-x), so +19.47 deg hav same kosine

Yu alwaes need tu test 180+-19.47...it mite giv same anser

Answer 2

Q: if sin x=-1/3 ⇒ sec x=?

A: cos x=±√(1-sin² x)=±√{1-(-1/3)²}=±√{1-(1/9)}=±√(8/9)

So, 1/cos x=1/±√(8/9)=±1√(9/8)=±√9/√8=±3/(2√2)=±(3√2)/4

Thus, sec x=1/cos x=±(3√2)/4

The answers are: sec x=(3√2)/4, or -(3√2)/4