Determining trigonometric ratios

I am relatively new to the concepts of trigonometry but have stumbled upon a problem. Is there an actual method to determine values of sine, cosine and tangent without using calculators?

#Trigonometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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Comments

It depends on the angle you're looking at. Could you be a bit more specific? I don't want to go into too much detail.

Bob Krueger - 7 years, 5 months ago

I mean angles under 180 degrees. I am asking for the actual method or formula to determine the values.

Sharky Kesa - 7 years, 5 months ago

it depends on what values are you searching. Some values like 30, 45, 60, 18, 36, 54, 72 and their relatives in the other quafdrants can be determined using basic geometry basic geometry, other ones can be also found using trigonometry relations

Jordi Bosch - 7 years, 5 months ago

@Jordi Bosch – Similarly, any multiple or half-angle thereof can be found in terms of algebraic expressions.

Bob Krueger - 7 years, 5 months ago

@Jordi Bosch – say, like 52 or 18. Do they share a common method?

Sharky Kesa - 7 years, 5 months ago

@Sharky Kesa – Well, 30, 45, and 60 are the basic ones. For 52 or 18, look up info about the golden ratio and these numbers.

Bob Krueger - 7 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$