Home > Trigonometry > Law of sines & Law of cosines

Law of sines & Law of cosines

Proovement of law of sines and cosines.

Law of sines

b \cdot sin \alpha = h , a \cdot sin \beta = h \Rightarrow

\Rightarrow b \cdot sin \alpha = a \cdot \sin \beta \Rightarrow

\Rightarrow \frac{ b }{ sin \beta } = \frac{ a }{ sin \alpha }

Law of cosines

BH = a \cdot cos \beta , AH = c - a \cdot cos \beta

h^2 = a^2 - a^2 \cdot cos^2 \beta \: and \: h^2 = b^2 - c^2 - a^2 \cdot cos^2 \beta + 2ac \cdot cos \beta

b^2 = a^2 + c^2 - 2ac \cdot cos \beta

Advertisements
Categories: Trigonometry Tags: ,
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Please log in using one of these methods to post your comment:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: