Respuesta :
The right angle triangle with 30-60-90 degrees is the special triangle in which these angle will have the side ratio of 1, [tex]\sqrt{3} [/tex] and 2. The value of the [tex] \cos\dfrac{(-2\pi)}{3} [/tex] which Omar wants to determine is -1/2.
Given information-
Omar wants to determine the value of
[tex] \cos\dfrac{(-2\pi)}{3} [/tex]
As the degree is in the pi form. Use the conversion rate [tex]\dfrac{180}{\pi} [/tex] to convert the degree,
[tex]=\dfrac{(-2\pi)}{3} \times\dfrac{180}{\pi} [/tex]
[tex]=-120[/tex]
As the angle -120 degrees is in the third quadrant hence the reference angle is 60 degrees(by calculating as (180-theta).
30-60-90 triangle
Now the right angle triangle with 30-60-90 degrees measure angle. Such angle will have the side ratio of 1, [tex]\sqrt{3} [/tex] and 2.
Here 2 is the hypotenuse of the right triangle. The side opposite to the angle measure [tex]\sqrt{3} [/tex] and the side adjacent to the angle measures 1 in ratio.
Now the cos theta is the ratio of the adjacent side and hypotenuse thus,
[tex] \cos\dfrac{(-2\pi)}{3} =-\dfrac{1}{2} [/tex]
Negative sign is used for the third quadrant where x axis is negative.
[tex] \cos\dfrac{(-2\pi)}{3} =-\dfrac{1}{2} [/tex]
Thus the value of the [tex] \cos\dfrac{(-2\pi)}{3} [/tex] which Omar wants to determine is -1/2.
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