| | 0∘ | 30∘ | 45∘ | 60∘ | 90∘ | 180∘ |
| sinα | 0 | 21 | 22 | 23 | 1 | 0 |
| cosα | 1 | 23 | 22 | 21 | 0 | −1 |
| tg α | 0 | 33 | 1 | 3 | nie istnieje | 0
|
| Jeśli kąt α jest kątem ostrym, to: sin(180∘−α)=sinα cos(180∘−α)=−cosα tg (180∘−α)=−tg α oraz sin(90∘−α)=cosα cos(90∘−α)=sinα tg (90∘−α)=tg α1 |
a) 3sin120∘⋅tg 135∘⋅cos60∘=
=3sin(180∘−60∘)⋅tg (180∘−45∘)⋅cos60∘=
=3sin60∘⋅(−tg 45∘)⋅cos60∘=
=3⋅23⋅(−1)⋅21=−433
b) 2cos2135∘−tg 60∘=
=2cos2(180∘−45∘)−tg 60∘=
=2⋅(−cos45∘)2−tg 60∘=
=2⋅(−22)2−3=2⋅42−3=1−3
c) (1−sin150∘)(1+sin150∘)=
=(1−sin(180∘−30∘))(1+sin(180∘−30∘))=
=(1−sin30∘)(1+sin30∘)=
=12−sin230∘=
=1−(21)2=1−41=43
d) sin2135∘+cos245∘=
=sin2(180∘−45∘)+cos245∘=
=sin245∘+cos245∘=
Korzystamy z jedynka trygonometrycznej.
=1
e) tg 148∘cos148∘+cos32∘=
=tg 148∘cos(180∘−32∘)+cos32∘=
=tg 148∘−cos32∘+cos32∘=
=tg 148∘0=0
f) tg 50∘⋅tg 45∘⋅tg 40∘=
=tg (90∘−40∘)⋅tg 45∘⋅tg 40∘=
=tg 40∘1⋅tg 45∘⋅tg 40∘=
=tg 45∘=1
g) tg 130∘⋅tg 135∘⋅tg 140∘=
=tg (180∘−50∘)⋅tg (180∘−45∘)⋅tg (180∘−40∘)=
=−tg 50∘⋅(−tg 45∘)⋅(−tg 40∘)=
=−tg 50∘⋅tg 45∘⋅tg 40∘=
=−tg (90∘−40∘)⋅tg 45∘⋅tg 40∘=
=−tg 40∘1⋅tg 45∘⋅tg 40∘=
=−tg 45∘=−1
