Find the value of $sec(fracpi4)$

To find the value of $\sec (\frac{\pi }{4})$, we first find the value of $\cos (\frac{\pi }{4})$. The cosine of $\frac{\pi }{4}$ is $\frac{\sqrt{2}}{2}$. Recall that $\sec (x)=\frac{1}{\cos (x)}$, so:

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

To calculate $sec(0)$, we need to know the value of $cos(0)$. We know that $cos(0)=1$. By the definition of secant, $sec(x)=frac1cos(x)$, so:

$sec(0)=frac1cos(0)=frac11=1$

To determine $\sec (\frac{\pi }{3})$, we find $\cos (\frac{\pi }{3})$. We know that $\cos (\frac{\pi }{3})=\frac{1}{2}$. Since $\sec (x)=\frac{1}{\cos (x)}$, we get:

$$\sec (\frac{\pi }{3})=\frac{1}{\cos (\frac{\pi }{3})}=\frac{1}{\frac{1}{2}}=2$$

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