How do you evaluate sec ((3pi) / 2)?

1 Answer
Zor Shekhtman
Apr 28, 2015

First of all, recall the definition of sec:
sec(alpha)=1/cos(alpha)

To determine cos((3pi)/2), recall the definition of cos based on a concept of a unit circle:

cos(alpha) is an abscissa (X-coordinate) of a point on a unit circle, which radius makes an angle alpha with a positive direction of the X-axis, counting from that positive direction of X-axis counter-clockwise.

Angle (3pi)/2 corresponds to a point with coordinates (0,-1) on a unit circle.
Therefore, cos((3pi)/2)=0.

Since sec((3pi)/2)=1/cos((3pi)/2) and cos((3pi)/2)=0, the value of sec((3pi)/2) is undefined.

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