Question
determine the exact value for cos13pi/12
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GPT 3.5
To determine the exact value for cos(13π/12), we need to use the unit circle and the reference angle.
The reference angle for 13π/12 is π/12.
Looking at the unit circle, we can see that the point corresponding to π/12 is (cosπ/12, sinπ/12).
Since cosπ/12 lies on the x-axis, its y-coordinate is 0. Therefore, cosπ/12 is equal to the x-coordinate of the point, which is (√3 - 1) / 2.
So, cos(13π/12) = cosπ/12 = (√3 - 1) / 2.
The reference angle for 13π/12 is π/12.
Looking at the unit circle, we can see that the point corresponding to π/12 is (cosπ/12, sinπ/12).
Since cosπ/12 lies on the x-axis, its y-coordinate is 0. Therefore, cosπ/12 is equal to the x-coordinate of the point, which is (√3 - 1) / 2.
So, cos(13π/12) = cosπ/12 = (√3 - 1) / 2.
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