Find the exact sine value of the angle in standard position whose terminal side goes through the point (-1,5)

I do not know when to start

To find the exact sine value of the angle in standard position whose terminal side goes through the point (-1,5), you can follow these steps:

Step 1: Plot the point (-1,5) on the Cartesian coordinate plane.

Step 2: Draw a line segment from the origin (0,0) to the point (-1,5). This line represents the terminal side of the angle.

Step 3: Determine the length of the hypotenuse of the right triangle formed by the line segment and the x-axis. You can use the Pythagorean theorem to find this length.

In this case, the length of the hypotenuse can be found as follows:
hypotenuse = sqrt((-1)^2 + 5^2)
= sqrt(1 + 25)
= sqrt(26)

Step 4: Determine the length of the side adjacent to the angle, which is the x-coordinate of the given point. In this case, the x-coordinate is -1.

Step 5: Use the trigonometric definition of sine to find the sine value of the angle. The sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

In this case, the side opposite to the angle is the y-coordinate of the given point, which is 5. Therefore, the sine value can be calculated as:
sine = opposite/hypotenuse
= 5/sqrt(26)

Therefore, the exact sine value of the angle in standard position whose terminal side goes through the point (-1,5) is 5/√26.