How do you evaluate the expression cos(60°) × cos(30°) × sin(60°) × sin(30°)?

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To evaluate the expression cos(60°) × cos(30°) × sin(60°) × sin(30°), we can start by calculating the trigonometric values for each angle involved.

  • cos(60°): The cosine of 60 degrees is 0.5.
  • cos(30°): The cosine of 30 degrees is approximately 0.866 or \\( rac{
    oot{3}}{2}\\).
  • sin(60°): The sine of 60 degrees is approximately 0.866 or \\( rac{
    oot{3}}{2}\\).
  • sin(30°): The sine of 30 degrees is 0.5.

Now that we have the values, we can substitute them into the expression:

cos(60°) × cos(30°) × sin(60°) × sin(30°)
= 0.5 × 0.866 × 0.866 × 0.5

Let’s simplify this step by step:

  1. First, we can calculate the product of the first two factors: 0.5 × 0.866.
    • 0.5 × 0.866 = 0.433
  2. Next, calculate the product of the last two factors: 0.866 × 0.5.
    • 0.866 × 0.5 = 0.433
  3. Finally, multiply the results of those two calculations: 0.433 × 0.433.
    • 0.433 × 0.433 ≈ 0.187

So, the final result of evaluating cos(60°) × cos(30°) × sin(60°) × sin(30°) is approximately 0.187.

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