Answer:
[tex]\sin \theta=-\frac{4}{5}[/tex]
Step-by-step explanation:
Given:
Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).
So, the 'x' value is 3 and 'y' value id -4.
Using Pythagoras Theorem, we find the hypotenuse.
Hypotenuse = [tex]\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]
Now, using the sine ratio for the angle, we have
[tex]\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}[/tex]
Therefore, the value of [tex]\sin \theta[/tex] is [tex]-\frac{4}{5}[/tex].
The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,
