A physicist needs to calculate the exact value of a force (measured in newtons) in the horizontal direction with the expression 25 cos 75 degrees. Simplify this expression to find the exact value.

To simplify the expression 25 cos 75 degrees, we first convert 75 degrees to radians:

75 degrees = 75 * π / 180 = 5π / 12 radians

Now, we can calculate the cosine of 5π / 12:

cos(5π / 12) ≈ 0.2588

Finally, we multiply this result by 25 to find the exact value of the force in the horizontal direction:

25 * 0.2588 ≈ 6.47 newtons

Therefore, the exact value of the force in the horizontal direction is approximately 6.47 newtons.