Question

Find tan(13pi/4)-cos(pi/3)

Answer 1

Answer: $tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}$

Step-by-step explanation:

To find $tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})$, we first need to understand the unit circle. Let's find the value of tan and cos before we subtract them.

$tan(\frac{13\pi }{4} )$ is the same as $tan(\frac{5\pi }{4} )$. The point for $\frac{5\pi }{4}$ is (-0.5,-0.5). Tangent is $\frac{sin}{cos}$. Since sin and cos are both -0.5, we can divide them.

$\frac{-0.5}{-0.5} =1$

Now, we know that $tan(\frac{13\pi }{4} )=1$. All we have to do is find $cos(\frac{\pi }{3})$.

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

Now that we know the values of both, we can directly subtract them.

1-0.5=0.5

Therefore, $tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}$.