cosine 180 degrees

Understand the Problem

The question is asking for the value of the cosine function at 180 degrees, which pertains to basic trigonometric functions.

Answer

-1
Answer for screen readers

The cosine of 180 degrees is -1

Steps to Solve

  1. Understand the cosine function on the unit circle

The cosine of an angle in the unit circle is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.

  1. Locate 180 degrees on the unit circle

180 degrees is located directly on the negative x-axis.

  1. Determine the coordinates at 180 degrees

The coordinates at 180 degrees on the unit circle are (-1, 0).

  1. Find the cosine value

The cosine of 180 degrees is the x-coordinate of this point, which is -1.

The cosine of 180 degrees is -1

More Information

A fun fact is that the cosine function is even, which means $\cos(-x) = \cos(x)$. So $\cos(180^{\circ}) = \cos(-180^{\circ}) = -1$.

Tips

A common mistake is confusing sine and cosine values. Remember on the unit circle, cosine corresponds to the x-coordinate and sine to the y-coordinate.

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