## anonymous 5 years ago find the value of tan 5π/8

1. amistre64

well; we can either try to se trig formulas; or simply use a calculator

2. amistre64
3. anonymous

oh, sorry. no calculators, says to use trig functions.

4. amistre64

you wanna use either a tan(a+b) or a tan(a-b) formula than; and find 2 angles that either add to or subtract to 5pi/8

5. anonymous

nice website, thanks

6. amistre64

tana+tanb tan(a+b) = ------------- 1- tana.tanb tana-tanb tan(a-b) = ------------- 1+ tana.tanb

7. amistre64

tan(2a) = 2.tana --------- 1-tan^2(a)

8. amistre64

but i dont see that one being helpful :)

9. amistre64

i dont se any of the familiar angles summing it up to get 112.5

10. amistre64

it is 225 degrees/2 tho; so maybe split that tan into sin and cos functions and work on half angle formulas

11. amistre64

either way you go, its gonna be a nightmare

12. anonymous

i know, but it looks like it would be so easy!

13. anonymous

thanks for trying

14. amistre64

it might be; but youd have to do allllooooottt of typing; and its just not that fun to try to keep track of on a keyboard

15. amistre64

sqrt(1+cos(5pi/4)) ----------------- = tan(5pi/8) sqrt(1-cos(5pi/4))

16. amistre64

sqrt(1+[-1/sqrt(2)]) ------------------- sqrt(1 - [1/sqrt(2)])

17. amistre64

$\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$

18. amistre64

thats the exact form

19. amistre64

well; i think it finally settles down to: -1 - sqrt(2)