Question

If 0 is an angle in standard position and its terminal side passes through the point

(5,-12), find the exact value of sin 0 in simplest radical form. plsplsplsplshelpppmeeee

Answer 1

Answer: the exact value of sin 0 in simplest radical form is -12/13.

Explanation:

To find the exact value of sin 0 in simplest radical form, we can use the coordinates of the point (5, -12) where the terminal side of the angle passes through.

We know that sin 0 is equal to the y-coordinate of the point divided by the length of the hypotenuse. To find the length of the hypotenuse, we can use the Pythagorean theorem.

Given that the coordinates are (5, -12), we have the following:

x = 5

y = -12

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h = √(x² + y²)

h = √(5² + (-12)²)

h = √(25 + 144)

h = √169

h = 13

Now, we can find sin 0:

sin 0 = y / h

sin 0 = -12 / 13