To find the value of sin(θ) where θ is the angle in standard position that has its terminal side passing through the point (15, 8), we first need to recognize that we can use the coordinates of this point to determine the sine of the angle.
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In our case, we can treat the coordinates (15, 8) as the lengths of the sides of a right triangle, where:
- The x-coordinate (15) represents the adjacent side.
- The y-coordinate (8) represents the opposite side.
Next, we need to find the hypotenuse (r) of the triangle using the Pythagorean theorem:
r = √(x² + y²)
Substituting our values:
r = √(15² + 8²) = √(225 + 64) = √289 = 17
Now we can find sin(θ):
sin(θ) = opposite/hypotenuse = y/r = 8/17
Thus, the value of sin(8) when considering the angle’s position is approximately 0.4706.