Answer:
A
Step-by-step explanation:
[tex]\cos(\theta)=\dfrac{\textsf{adjacent side}}{\textsf{hypotenuse}}=\dfrac{5}{13}[/tex]
[tex]\textsf{As }\cos(\theta) > 0 \textsf{ the angle is in quadrant I or IV}[/tex]
Using Pythagoras' Theorem a² + b² = c² to find the side opposite the angle:
⇒ 5² + b² = 13²
⇒ b² = 144
⇒ b = 12
⇒ opposite side = 12
[tex]\implies \sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}=\dfrac{12}{13}[/tex]
[tex]\textsf{As }\sin(\theta) < 0 \textsf{ then }\sin(\theta)=-\dfrac{12}{13} \textsf{ and the angle is in either quadrant III or quadrant IV}[/tex]
Therefore, the common quadrant is quadrant IV and
[tex]\sin(\theta)=-\dfrac{12}{13}[/tex]
