Home  18.013A  Chapter 2  Section 2.2 


Derive the relations between these functions by using similar triangles.
Solution:
By similar triangles, the ratio of BD to BO, $\mathrm{sin}\theta $ to 1 is the same as the ratio of CB to OC, $\mathrm{tan}\theta $ to $\mathrm{sec}\theta $ , and of OB to AO (1 to $\mathrm{csc}\theta $ ), and of CO to AC ( $sec\theta $ to ( $\mathrm{tan}\theta +\mathrm{cot}\theta $ )), and of CD to BC (( $\mathrm{sec}\theta \mathrm{cos}\theta $ ) to $\mathrm{tan}\theta $ ), and of OE to BO ( $\mathrm{sin}\theta $ to 1)
This tells us
so that on taking complements we have as well,
We also get
and the complementary result
