Problem 72
Question
In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\tan \frac{9 \pi}{2}$$
Step-by-Step Solution
Verified Answer
\(\tan(\frac{9\pi}{2})\) is undefined
1Step 1: Identifying the quadrant and reference angle
In order to evaluate the expression, the first step is to find where the angle \(\frac{9\pi}{2}\) lies on the unit circle. Remember that \(\frac{2\pi}{2} = \pi\) represents a complete revolution around the unit circle. Therefore, \(\frac{9\pi}{2} = 4\pi + \frac{\pi}{2}\). This is the same as making 4 complete revolutions around the circle and then moving an additional \(\frac{\pi}{2}\) radians, which ends in the positive y-axis.
2Step 2: Evaluating Tangent Function
Once we know where the angle ends up, we know that the reference angle is 0, because we end up at the positive y-axis, moving counter-clockwise. The point on the unit circle corresponding to this angle is \((0,1)\). The tangent of an angle in the unit circle is the ratio of the y-coordinate to the x-coordinate. In this case, the x-coordinate is 0 and the y-coordinate is 1. Therefore, \(\tan(\frac{9\pi}{2})\) is undefined because we cannot divide by zero.
Other exercises in this chapter
Problem 72
Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sine and cosine are cofunctions and reciprocals of each oth
View solution Problem 72
Find the length of the arc on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). Express arc length in terms of \(\pi .\) Then rou
View solution Problem 72
Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is def
View solution Problem 72
Let $$ \sin t=a, \cos t=b, \text { and } \tan t=c $$ Write each expression in terms of \(a, b,\) and \(c\). $$\tan (-t)-\tan t$$
View solution