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Chapter 4: Problem 40

Use the value of the trigonometric function to evaluate the indicated functions. \(\cos t=-\frac{3}{4}\) (a) \(\cos (-t)\) (b) \(\sec (-t)\)

Short Answer

Expert verified
\(\cos(-t) = -\frac{3}{4}\), \(\sec(-t) = -\frac{4}{3}\)

Step by step solution

01

Evaluate \(\cos(-t)\)

It is known that cosine is an even function, this means that it holds the property \(\cos(-t) = \cos(t)\). Given that \(\cos(t) = -\frac{3}{4}\), to find \(\cos(-t)\) one just needs to consider that \(\cos(-t) = \cos(t)\), hence \(\cos(-t) = -\frac{3}{4}\)
02

Evaluate \(\sec(-t)\)

Now for the secant of -t. Recall that secant is just the reciprocal of the cosine function. So, \(\sec(t) = \frac{1}{\cos(t)}\). Since we found that \(\cos(-t) = \cos(t)\) in Step 1, we know that \(\sec(-t) = \frac{1}{\cos(-t)}\). Substitute \(\cos(-t) = -\frac{3}{4}\) into the equation to get \(\sec(-t) = -\frac{4}{3}\)

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