evaluate without a calculator: sec\\frac{3\\pi}{4} type + or -

Explanation:

Step1: Recall the definition of secant

(\sec x=\frac{1}{\cos x}), so (\sec\frac{3\pi}{4}=\frac{1}{\cos\frac{3\pi}{4}})

Step2: Find the value of (\cos\frac{3\pi}{4})

(\frac{3\pi}{4}) is in the second quadrant. (\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2})

Step3: Calculate (\sec\frac{3\pi}{4})

(\sec\frac{3\pi}{4}=\frac{1}{\cos\frac{3\pi}{4}}=\frac{1}{-\frac{\sqrt{2}}{2}}=-\sqrt{2})

Answer:

• (\sqrt{2})