Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Angle θ is in standard position and (4,4) is a point on the terminal side of θ.
[tex]\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}[/tex]
Now, secant is the inverse of cosine.
Therefore:
[tex]\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}[/tex]
