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
- 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.
- Locate 180 degrees on the unit circle
180 degrees is located directly on the negative x-axis.
- Determine the coordinates at 180 degrees
The coordinates at 180 degrees on the unit circle are (-1, 0).
- 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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