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.