Algebra-2

The terminal side of in standard position contains the point . We want to find the value of .

 

To find the value of , we need to determine the reciprocal of the sine function for the angle in the right triangle formed by the point .

 

Given that the point lies on the terminal side of the angle , we can use these coordinates to determine the lengths of the sides of the triangle.

 

The opposite side is the side opposite to the angle and is the vertical side of the triangle. In this case, the opposite side has a length of 40, which corresponds to the absolute value of the -coordinate.

 

Now we can calculate the value of :

 

 

To find the value of , we need to normalize the opposite side by the hypotenuse. We can use the Pythagorean theorem to find the hypotenuse:

 

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