To compute [tex]\(\cos \left(-\frac{7 \pi}{12}\right)\)[/tex], follow these steps:
1. Recognize the Property of the Cosine Function: The cosine function is an even function, meaning [tex]\(\cos(-x) = \cos(x)\)[/tex] for any angle [tex]\(x\)[/tex]. This property allows us to simplify the problem:
[tex]\[
\cos \left(-\frac{7 \pi}{12}\right) = \cos \left(\frac{7 \pi}{12}\right)
\][/tex]
2. Evaluate the Cosine of the Positive Angle: We need to find the value of [tex]\(\cos \left(\frac{7 \pi}{12}\right)\)[/tex].
3. Numerical Result: The value of [tex]\(\cos \left(\frac{7 \pi}{12}\right)\)[/tex] is approximately:
[tex]\[
\cos \left(\frac{7 \pi}{12}\right) \approx -0.25881904510252063
\][/tex]
Thus, the cosine of [tex]\(-\frac{7\pi}{12}\)[/tex] is:
[tex]\[
\cos \left(-\frac{7\pi}{12}\right) = -0.25881904510252063
\][/tex]
