Problem 47 - Precalculus Essentials

Question

Find the exact value of each trigonometric function. Do not use a calculator. $$-\tan \left(\frac{\pi}{4}+15 \pi\right)$$

Step-by-Step Solution

Answer

The exact value of the given trigonometric function is \(-1\)

Step 1: Simplify the angle

The angle in the tangent function is \(\frac{\pi}{4} + 15\pi\). However, because \(\pi\) is a period of the tangent function, we can disregard multiples of \(\pi\) when calculating the tangent of an angle. Therefore, we simplify the angle to \(\frac{\pi}{4}\)

Step 2: Calculate the tangent of the simplified angle

Next, we calculate the tangent of \(\frac{\pi}{4}\). We know that \(\tan(\frac{\pi}{4}) = 1\). Thus, the result of our calculation is 1

Step 3: Apply the negative sign

Don't forget the negative sign. Thus, our final answer is \(-1\)