Answer:
Option B
Explanation:
Given that:
[tex]\text{Terminal point of }\theta=(\frac{1}{2},\frac{\sqrt[]{3}}{2})[/tex]
If P(x, y) is the terminal point of an angle, then x is the length of its adjacent side and y is the length of its opposite side.
Here,
[tex]\begin{gathered} \text{Length of adjacent side =}\frac{1}{2} \\ \text{Length of opposite side =}\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]
First, find the length of hypotenuse using the Pythagorean theorem.
[tex]\begin{gathered} \text{Hypotenuse}^2=Adjacentside^2+Oppositeside^2 \\ =(\frac{1}{2})^2+(\frac{\sqrt[]{3}}{2})^2 \\ =\frac{1}{4}+\frac{3}{4} \\ =1 \\ \text{Hypotenuse}=\sqrt[]{1}=1 \end{gathered}[/tex]
Using the trigonometric ratio,
[tex]cos\theta=\frac{\text{Adjacent side}}{Hypotenuse}[/tex]
Plug the values into the formula.
[tex]\begin{gathered} cos\theta=\frac{\frac{1}{2}}{1} \\ =\frac{1}{2} \end{gathered}[/tex]
Hence, option B is correct.
