# What is the value of tan (pi/4)?

Math Staff asked 4 months ago

$\ tan(\frac{\pi}{4}) = 1$

#### Explanation:

$\ \pi = 180$

$\ \frac{\pi}{4} = 45$

Using the identity

$\ tan = \frac{sin}{cos}$

$\ sin(\frac{\pi}{4}) = \frac{\sqrt {2}}{2}$

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

$\ tan(\frac{\pi}{4}) = \frac{\frac{\sqrt {2}}{2}}{\frac{\sqrt {2}}{2}}$

$\ tan(\frac{\pi}{4}) = \frac{\sqrt {2}}{2} \times \frac{2}{\sqrt {2}}$

Cancelling rationalising the denominator

$\ tan(\frac{\pi}{4}) = 1$