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

Math Staff asked 2 months ago

Answer:

\[\ tan(\frac{\pi}{4}) = 1 \]

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

\[\ tan(\frac{\pi}{4}) = 1 \]