Question

Angle θ is in standard position and ( 4 , 4 ) is a point on the terminal side of θ. What is the exact value of sec ⁡ θ sec 0 in simplest form with a rational denominator?

Answer 1

`√(2)`

Explanation:

Angle θ is in standard position and (4,4) is a point on the terminal side of θ.

`\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=√(32)=4√(2)`

Now, secant is the inverse of cosine.

Therefore:

`\sec \theta =(Hypotenuse)/(Adjacent) \\\sec \theta =(4√(2))/(4) \\\sec \theta =√(2)`