Problem 46 - Precalculus: A Concise Course

Question

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

Step-by-Step Solution

Answer

The value of \(\cos (-t)\) is -\frac{3}{4} and the value of \(\sec (-t)\) is -\frac{4}{3}.

Step 1: Evaluate \(\cos (-t)\)

The cosine function has a property known as being 'even'. This means that \(\cos (-t) = \cos t\). Therefore, since \(\cos t = -\frac{3}{4}\), we can say that \(\cos (-t) = -\frac{3}{4}\).

Step 2: Evaluate \(\sec (-t)\)

The secant function \(\sec (x)\) is defined as the reciprocal of the cosine function, or \(\sec (x) = \frac{1}{\cos (x)}\). Therefore, using the value for \(\cos t = -\frac{3}{4}\) that we already have, we can find that \(\sec (-t) = -\frac{4}{3}\).