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

Answer:

$\sqrt{2}$

Step-by-step explanation:

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

$\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\ Using Pythagoras Theorem\\Hypotenuse^2= Opposite^2 +Adjacent^2\\ Hypotenuse^2=4^2+4^2\\ Hypotenuse^2 =32\\Hypotenuse=\sqrt{32}=4\sqrt{2}$

Now, secant is the inverse of cosine.

Therefore:

$\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}$