Find cos(theta) if (-15, 8) is a point of the terminal side of theta.
=-15/sqrt((-15)^2+8^2)
To find the value of cos(theta), where (-15, 8) is a point on the terminal side of theta, we can use the definition of trigonometric functions in a right triangle.
First, let's draw a right-angled triangle with the given point (-15, 8) as one of the vertices on the terminal side of theta. The x-coordinate (-15) represents the horizontal distance (adjacent side) from the origin (0,0) to the point, and the y-coordinate (8) represents the vertical distance (opposite side).
Next, we need to determine the length of the hypotenuse, which can be found using the Pythagorean theorem. The hypotenuse, denoted as r, is the square root of the sum of the squares of the lengths of the other two sides. In this case:
r = sqrt((-15)^2 + (8)^2)
r = sqrt(225 + 64)
r = sqrt(289)
r = 17
Now that we know the lengths of the sides of the triangle, we can find the value of cos(theta) using the adjacent side and the hypotenuse.
cos(theta) = adjacent side / hypotenuse
cos(theta) = -15 / 17
cos(theta) ≈ -0.8824
Therefore, cos(theta) ≈ -0.8824, when (-15, 8) is a point on the terminal side of theta.