Chapter 13 - The Trigonometric Functions - 13.1 Definitions of the Trigonometric Functions - 13.1 Exercises - Page 678: 26

$sin 45^\circ = \frac{\sqrt 2}{2}$ $cos 45^\circ = \frac{\sqrt 2}{2}$ $csc 45^\circ =\sqrt 2$ $sec 45^\circ =\sqrt 2$

From the table we have the following information: $tan 45^\circ=1$ $cot 45^\circ=1$ then, using the elementary trigonometric identities we obtain: $sin 45^\circ =\frac{1}{\sqrt 2}=\frac{\sqrt 2}{2}$ $cos 45^\circ =\frac{1}{\sqrt 2}=\frac{\sqrt 2}{2}$ $csc 45^\circ =\frac{1}{sin 45^\circ }=\sqrt 2$ $sec 45^\circ =\frac{1}{cos 45^\circ}=\sqrt 2$