Mysterious Art of Handling Trigonometric Ratios

Weeks back, when I first had my trigonometric lesson, I was taught the simple basic identities of trigonometric ratios for special angles such as 30030^0, 45045^0 and 60060^0 not forgetting right angles and zeroes too. Then it hit me, while I may had basic prior knowledge of trigonometry back then before the new lesson, I wondered how did trigonometric ratios such as tan,cosandsintan, cos and sin even came about in the first place? Is there a certain pattern or formula or any other that may allow me to retrieve the values of Trigo. ratios for any angles quickly without the use of calculator? Is it possible to mentally calculate trigonometric ratios for any angle as fast as multiplying numerical values such as 5×75\times 7? Though I know it is pretty hard to answer it now or there may not even be an answer to these questions. However, I believe in time to come, the secret to mental calculation of trigo. ratios may be discovered. I hope the note isn't overly-ambitious on the impossible....

Note by Jonathan Chee
4 years, 6 months ago

No vote yet
1 vote

</code>...<code></code> ... <code>.">   Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in </span>...<span></span> ... <span> or </span>...<span></span> ... <span> to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest

Use the infinite expansion of both sin \sin and cos \cos if you don't have calculator. At least you would get approximate answer using only a few terms. For problems, usually the ratios can be found using sum and difference, double angle and half angle, etc.

Marc Vince Casimiro - 4 years, 6 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...