Question

The point (8, –15) is on the terminal side of an angle θ. What is sin θ ?

Answer 1

For the answer to the question What is sin θ ? (8, -15) is in quadrant IV. 

Draw the right triangle. 
hypotenuse = √(8² + 15²) = 17 
sinθ = -15/17 

Just draw the graph for reference.

I hope my answer helped you. Feel free to ask more questions. Have a nice day!

Answer 2

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  $-\frac{15}{17}$.