Problem 45

Question

Use the value of the trigonometric function to evaluate the indicated functions. \(\cos (-t)=-\frac{1}{5}\) (a) \(\cos t\) (b) \(\sec (-t)\)

Step-by-Step Solution

Verified
Answer
\(\cos(t) = -1/5\) and \(\sec(-t) = -5\).
1Step 1: Determine \(\cos(t)\)
For any real number t, \(\cos(t) = \cos(-t)\) because cosine is an even function. So, \(\cos(t) = -\frac{1}{5}\).
2Step 2: Compute \(\sec(-t)\)
Since the secant function is the reciprocal of the cosine function, to find \(\sec(-t)\), take the reciprocal of \(-1/5\). Therefore, \(\sec(-t) = -5\).