Answer:
Step-by-step explanation:
We'll use the half angle identity for tangent along with the unit circle to find the exact value of tan(π / 4). There are 3 half angle identities for tangent, but I chose this one (just because!):
[tex]tan(\frac{\theta}{2})=\frac{1-cos\theta}{sin\theta}[/tex]
We just need to find the angle to replace theta. It will be
[tex]tan(\frac{\frac{\pi}{2} }{2})[/tex] because
[tex]\frac{\pi}{2} *\frac{1}{2}=\frac{\pi}{4}[/tex]
Filling in:
[tex]tan(\frac{\frac{\pi}{2} }{2})=\frac{1-cos(\frac{\pi}{2}) }{sin(\frac{\pi}{2}) }[/tex]
Here's where we'll look to the unit circle to find that the
[tex]cos(\frac{\pi}{2})=0[/tex] and [tex]sin(\frac{\pi}{2})=1[/tex] so filling those values in gives us:
[tex]tan(\frac{\frac{\pi}{2} }{2})=\frac{1-0}{1}[/tex] so the exact value of
[tex]tan(\frac{\pi}{4})=1[/tex]
