Answer:
\(\sin \theta = -\frac{15}{17}\)
Step-by-step explanation:
Given the point (8, -15) is on the terminal side of an angle \(\theta\).
To find the value of \(\sin \theta\).
As the point (8, -15) lies in the fourth quadrant where \(\sin \theta < 0\)
In a right angle triangle;
here, adjacent side = x = 8 units and Opposite side = y = -15 units
Using Pythagoras theorem;
\((Hypotenuse side)^2 = (Adjacent side)^2+(Opposite side)^2\)
Substitute the given values we have;
\((Hypotenuse side)^2 = (8)^2+(-15)^2\)
\((Hypotenuse side)^2 = 64+ 225 = 289\)
\(Hypotenuse side = \sqrt{289} =17 units\)
Sine ratio is defined as in the right angle triangle, the ratio of opposite side to Hypotenuse side.
\(\sin \theta = \frac{Opposite side}{Hypotenuse side}\)
then;
\(\sin \theta = -\frac{15}{17}\)
therefore, the value of \(\sin \theta\) is \(-\frac{15}{17}\).
