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Chapter 4: Problem 42

Use the value of the trigonometric function to evaluate the indicated functions. \(\cos t=\frac{4}{5}\) (a) \(\cos (\pi-t)\) (b) \(\cos (t+\pi)\)

Short Answer

Expert verified
(a) \(\cos (\pi - t) = - \frac{4}{5}\) and (b) \(\cos (t + \pi) = - \frac{4}{5}\)

Step by step solution

01

Finding \(\cos (\pi-t)\)

We know from the property of symmetry of the cosine function that \(\cos (\pi - t) = - \cos t\). So, we substitute \(t\) with the given value \( \frac{4}{5} \). Therefore, \(\cos (\pi - t) = -\cos t = -\frac{4}{5}\).
02

Finding \(\cos (t+\pi)\)

From the property of periodicity of the cosine function, we have \(\cos (t + \pi) = - \cos t\). Now, substituting \(t\) with the given value \( \frac{4}{5} \), results in \(\cos (t + \pi) = - \cos t = - \frac{4}{5} \).

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