how does tan(5pi/4) = 1

Question

anonymous · Answer

because sine and cosine are the same number there

anonymous · Answer

how do you know that?

b87lar · Answer

tan has a period of pi, so tan(x+pi) = tan(x)

dannyo19 · Answer

tan(5pi/4)= sin(5pi/4)/cos(5pi/4)

b87lar · Answer

and tan(1/4 pi) = 1

dannyo19 · Answer

So add a pi to 1/4pi and you're back at 1 given it's period=pi

campbell_st · Answer

well $$\tan(\frac{5\pi}{4}) = \tan(\pi + \frac{\pi}{4})$$

so it's 3rd  quadrant where tan is positive

you can use the sum indentity to show

$$\tan(\pi + \frac{\pi}{4}) = \frac{\tan(\pi) + \tan(\frac{\pi}{4})}{1 - \tan(\pi)\times \tan(\frac{\pi}{4})}$$

hope that helps

anonymous · Answer

i know it because the corresponding point on the unit circle is $(\frac{-\sqrt2}{2},\frac{-\sqrt2}{2})$

anonymous · Answer

what you need is a nice unit circle cheat sheet

anonymous · Answer

attachment

anonymous · Answer

locate $\frac{5\pi}{4}$ on the unit circle on the last page of the attached cheat sheet
you will see that the first coordinate (cosine) and the second coordinate (sine) are the same there
that means that the tangent is one

anonymous · Answer

I wish I could medal all of you

anonymous · Answer

Thank you

campbell_st · Answer

sorry@satellite73, didn't mean to push in