Cos(11π/6)
To find the value of cos(11π/6), we first need to understand the unit circle and how it relates to trigonometric functions
To find the value of cos(11π/6), we first need to understand the unit circle and how it relates to trigonometric functions.
The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate plane. It is often used in trigonometry to understand the values of trigonometric functions for different angles.
In the unit circle, the angle is measured from the positive x-axis in the counterclockwise direction. So, when we have an angle in radians, like 11π/6, we can represent it as a fraction of the total circumference of the unit circle.
11π/6 is an angle that is close to 2π (or a full revolution around the circle). It is equivalent to 360 degrees/180 degrees, which means it is a little less than 2 full revolutions.
To find cos(11π/6), we need to find the x-coordinate of the point on the unit circle that corresponds to this angle. This x-coordinate represents the cosine value.
In the unit circle, at 11π/6, the terminal side of the angle will be in the fourth quadrant. This means the x-coordinate will be negative.
To find the exact value, we can break down 11π/6 into simpler fractions. We can write it as (10π/6 + π/6).
10π/6 is equal to 2π, which represents one complete revolution around the unit circle. So, adding π/6 to this gives us the angle slightly further than a full revolution.
Now, in the fourth quadrant, the reference angle (the acute angle formed between the x-axis and the terminal side) will be the supplement of π/6, which is 5π/6.
For any angle in the fourth quadrant, cos is positive. Therefore, cos(11π/6) is equal to the absolute value of cos(5π/6).
The cosine of 5π/6 is a well-known value. It represents a 30-degree angle, and at that angle, the cosine is equal to (√3)/2.
So, cos(11π/6) = |cos(5π/6)| = |(√3)/2| = √3/2.
Therefore, the value of cos(11π/6) is √3/2.
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