To evaluate cos 60° x cos 30° x sin 60° x sin 30°, we can start by determining the values of the trigonometric functions involved:
- cos 60° = 0.5
- cos 30° = √3/2
- sin 60° = √3/2
- sin 30° = 0.5
Now we plug these values into the expression:
First, calculate cos 60° x cos 30°:
0.5 x (√3/2) = (0.5√3)/2 = √3/4
Next, calculate sin 60° x sin 30°:
(√3/2) x 0.5 = (0.5√3)/2 = √3/4
Now we multiply the results:
(√3/4) x (√3/4) = (√3 x √3) / (4 x 4) = 3/16
Thus, the final result of evaluating cos 60° x cos 30° x sin 60° x sin 30° is 3/16.