Pierwiastek z tangensa

kamilos12 · Post autor: **kamilos12** » 31 mar 2010, o 16:42

Kąt \(\displaystyle{ \alpha}\) jest ostry i cos \(\displaystyle{ \alpha= \frac {8}{17}}\)
Oblicz \(\displaystyle{ \sqrt{\tg^2 \alpha + 1}\)

JakimPL · Post autor: **JakimPL** » 31 mar 2010, o 17:03

Wyznacz z jedynki trygonometrycznej \(\displaystyle{ \sin \alpha}\) i wylicz \(\displaystyle{ \tg \alpha}\).

sYa_TPS · Post autor: **sYa_TPS** » 31 mar 2010, o 17:45

kamilos12 pisze:Kąt \(\displaystyle{ \alpha}\) jest ostry i cos \(\displaystyle{ \alpha= \frac {8}{17}}\)
Oblicz \(\displaystyle{ \sqrt{\tg^2 \alpha + 1}\)

\(\displaystyle{ x/r = 8/17}\)

x = 8
r = 17

\(\displaystyle{ 64 + y^{2} = 289}\)

y = 15

tg = y/x = 15/8

\(\displaystyle{ \sqrt{225/64 + 64/64 } = \sqrt{289/64} = 17/8}\)