Answer: [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}[/tex]
Step-by-step explanation:
To find [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})[/tex], we first need to understand the unit circle. Let's find the value of tan and cos before we subtract them.
[tex]tan(\frac{13\pi }{4} )[/tex] is the same as [tex]tan(\frac{5\pi }{4} )[/tex]. The point for [tex]\frac{5\pi }{4}[/tex] is (-0.5,-0.5). Tangent is [tex]\frac{sin}{cos}[/tex]. Since sin and cos are both -0.5, we can divide them.
[tex]\frac{-0.5}{-0.5} =1[/tex]
Now, we know that [tex]tan(\frac{13\pi }{4} )=1[/tex]. All we have to do is find [tex]cos(\frac{\pi }{3})[/tex].
[tex]cos(\frac{\pi }{3})=\frac{1}{2}[/tex]
Now that we know the values of both, we can directly subtract them.
1-0.5=0.5
Therefore, [tex]tan(\frac{13\pi }{4})-cos(\frac{\pi }{3})=\frac{1}{2}[/tex].
