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.

Answer 1

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.