to 1 is the same as the ratio of CB to OC, tan
to sec,
and of OB to AO (1 to csc),
and of CO to AC (sec
to (tan
+ cot)),
and of CD to BC ((sec-
cos)
to tan),
and of OE to BO (sin
to 1)|
Home | 18.013A | Chapter 2 | Section 2.2 |
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Derive the relations between these functions by using similar triangles.
Solution:
By similar triangles, the ratio of BD to BO, sin
to 1 is the same as the ratio of CB to OC, tan
to sec,
and of OB to AO (1 to csc),
and of CO to AC (sec
to (tan
+ cot)),
and of CD to BC ((sec-
cos)
to tan),
and of OE to BO (sin
to 1)
This tells us
so that on taking complements we have as well,
We also get
and the complementary result
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