Understanding the Sine Function in Trigonometry
The primary aim is to find the sine of an angle where the terminal side of the angle intersects the point (15, 8). First, let’s understand the scenario involving the angle in standard position. The terminal side of the angle is determined by a point (x, y) in the Cartesian coordinate system. For this case, the coordinates are given as (15, 8).
Steps to Calculate sin(θ)
To find the value of sin(θ), we can utilize the relationship between the opposite side, the hypotenuse of the triangle formed, and the definition of the sine function.
- Identify the values:
Here, the coordinates are x = 15 and y = 8. The sine of θ is defined as the ratio of the length of the side opposite the angle (y) to the hypotenuse (r). - Calculate the hypotenuse:
We can calculate the hypotenuse using the Pythagorean theorem:
r = √(x² + y²) = √(15² + 8²) = √(225 + 64) = √289 = 17 - Calculate sin(θ):
Now that we have both the opposite side and the hypotenuse, we can determine the sine:
sin(θ) = y/r = 8/17
Final Value
Therefore, the value of sin(8) when the terminal side of the angle in standard position passes through the point (15, 8) is: 8/17.