# Find the sum of the smallest positive and largest negative roots of the equation cosx = √3 / 2.

May 30, 2021 | education

| 1. Let’s find the general solution of this trigonometric equation:

cosx = √3 / 2;

x = ± π / 6 + 2πk, k ∈ Z;

x1 = -π / 6 + 2πk, k ∈ Z;

x2 = π / 6 + 2πk, k ∈ Z.

2. The largest negative and smallest positive roots of the equation correspond to the values of x1 and x2 at k = 0:

x1 = -π / 6 + 2π * 0 = -π / 6;

x2 = π / 6 + 2π * 0 = π / 6.

3. The sum of these roots is zero:

x1 + x2 = -π / 6 + π / 6 = 0.

The answer is zero.

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