Have you ever wondered what is expressed just in x? Probably not, but it might actually sometimes be useful to know. The expression might for example turn up when you’ve done a trigonometric substitution in an integral. So I decided how to go about to show the trigonometric identities

,

,

.

The idea is the use the well known identity and try to get a relation between the basic trig functions and the arcus functions trough that. It goes like this

using the well known identity. We see that we already have the wanted relation, so that the rest is algebra. By squaring both sides we get

.

And there we have the first one. Similarly to obtain the next one we go

,

Obtaining the symmetric identity between sine and cosine. For tangent we go

where we separately use expression 3 and 4 in the equal-chain above to obtain

and then for nr.4

.

And that was that. Later i will do etc.. but that requires complex numbers.

Hehe takk for det Mathias 😉 Fortsett med det.

Du må bare si ifra hvis du har noen forslag til hva jeg kan skrive om.

Flott artikkel, Mikael! Jeg trenger alltid en liten trigonometri-repetisjon. Nå trenger jeg bare en liten gjennomgang av enhetssirkelen.

Det virker kanskje som om jeg leter etter oppdateringer på bloggen deres hele tiden, men jeg har faktisk en RSS-feed til e-postklienten min.

🙂