The function cos(x) is periodic, with a period of 2π radians or 360 degrees. This means that cos(x) = cos(x + 2π) for any value of x.
To find the measure of the angle whose cosine is -1/13, we can use the inverse cosine function (also called arccosine). The arccosine function gives the angle whose cosine is a given value.
arccos(-1/13) is the angle whose cosine is -1/13. We can use a calculator to find an approximate value of this angle:
arccos(-1/13) ≈ 100.96 degrees
Therefore, the measure of the angle whose cosine is -1/13 is approximately 101 degrees.