Question

evaluate without a calculator: sec 3π/4 type + or -

Explanation:

Step1: Convert secant to cosine

We know that $\sec\theta=\frac{1}{\cos\theta}$. So, $\sec\frac{3\pi}{4}=\frac{1}{\cos\frac{3\pi}{4}}$.

Step2: Find the value of cosine

The angle $\frac{3\pi}{4}$ is in the second quadrant. In the second quadrant, $\cos\theta<0$. And $\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}$.

Step3: Calculate the secant value

Substitute $\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}$ into $\sec\frac{3\pi}{4}=\frac{1}{\cos\frac{3\pi}{4}}$. Then $\sec\frac{3\pi}{4}=\frac{1}{-\frac{\sqrt{2}}{2}}=-\sqrt{2}$.

Answer:

• and 2.