What is the value of cos(120 degrees) and how can you find it?

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To find the value of cos(120^ ext{°}), we can use the unit circle and some trigonometric identities.

First, recognize that 120^ ext{°} is in the second quadrant of the unit circle. In this quadrant, the cosine value is negative. To find the cosine of 120^ ext{°}, we can relate it to a reference angle.

The reference angle for 120^ ext{°} is calculated as:

  • 180^ ext{°} - 120^ ext{°} = 60^ ext{°}

Knowing that the cosine of the reference angle gives us the absolute value, we can look up cos(60^ ext{°}:

  • cos(60^ ext{°}) = rac{1}{2}

Since 120^ ext{°} is in the second quadrant, the cosine will be negative. Therefore, we have:

  • cos(120^ ext{°}) = -cos(60^ ext{°}) = - rac{1}{2}

Putting it all together, the value of cos(120^ ext{°}) is -0.5.

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