Chapter 13, Trigonometric Ratios and Functions - 13.3 Evaluate Trigonometric Functions of Any Angle - 13.3 Exercises - Skill Practice - Page 871: 24

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Since $\cos(180-theta)=-\cos \theta$ we obtain $\cos(180-135)=-\cos 135\\\cos 45=-\cos 135\\-\cos 45=\cos 135\\\cos 135=-\frac{\sqrt 2}{2}$ Now find $\sec135=\frac{1}{\cos 135}=\frac{1}{-\frac{\sqrt 2}{2}}=-\frac{2}{\sqrt 2}=-\sqrt 2$