 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/7/b/solution

Using

sin (π /6) = 1/2

in the preceding half-angle identities gives

sin^{2} \frac{π}{12} = \frac{2 - 3}{4} \approx \frac{2 - 1.732}{4} = 0.067.

To two decimal places the answer is $0.07$ .

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