Problem 43 - Precalculus: A Concise Course

Question

Evaluate the trigonometric function of the quadrant angle. $$ \csc \pi $$

Step-by-Step Solution

Answer

\(\csc \pi\) is undefined.

Step 1: Recall the definition of cosecant

Cosecant function, denoted as \(\csc \theta\), is the reciprocal of the sine function. Hence, \(\csc \theta = 1/\sin \theta\).

Step 2: Convert the angle to degrees

The given angle is \(\pi\) radians. Remember that \(\pi\) radians is equivalent to 180 degrees. Hence, we want to find the value of \(\sin 180\).

Step 3: Evaluate the sine of 180 degrees

By definition of the unit circle, the sine of 180 degrees is 0. Hence, \(\sin 180 = 0\).

Step 4: Substitution and evaluation

Substitute \(\sin 180 = 0\) into \(\csc \theta = 1/\sin \theta\). Hence, we get \(\csc \pi = 1/0\). However, division by zero is undefined in mathematics.