Question

Cos510*cos600*cos780

Answer 1

Смотри вложение .............................

Answer 2

To calculate the value of the expression cos(510) * cos(600) * cos(780), you need to convert the angles from degrees to radians and then use the trigonometric identity that states:

cos(A) * cos(B) = (1/2) * [cos(A + B) + cos(A - B)]

Let's proceed with the calculations:

1. Convert angles from degrees to radians:

   • 510 degrees = (510 * π) / 180 ≈ 8.901 degrees
   • 600 degrees = (600 * π) / 180 ≈ 10.472 degrees
   • 780 degrees = (780 * π) / 180 ≈ 13.635 degrees

2. Apply the trigonometric identity: cos(510) * cos(600) * cos(780) = (1/2) * [cos(510 + 600) + cos(510 - 600)] * cos(780) = (1/2) * [cos(1110) + cos(-90)] * cos(780)

3. Evaluate the cosine values:

   • cos(1110) ≈ 0.1736 (rounded to four decimal places)
   • cos(-90) = 0 (cosine of negative 90 degrees is 0)

4. Plug the values back into the expression: cos(510) * cos(600) * cos(780) = (1/2) * [0.1736 + 0] * cos(780) ≈ 0.0868 * cos(780)

5. Calculate the value of cos(780): 780 degrees = (780 * π) / 180 ≈ 13.635 degrees cos(780) ≈ cos(13.635) ≈ 0.9781 (rounded to four decimal places)

6. Finally, multiply the values: cos(510) * cos(600) * cos(780) ≈ 0.0868 * 0.9781 ≈ 0.0849 (rounded to four decimal places)

So, cos(510) * cos(600) * cos(780) ≈ 0.0849.