is there any way we can figure out what sin(20) equals to without using a calculator?

Answer 1

draw a scale model where the angle is 20 degrees
then complete a proper right triangle(the other angle should be 70) and measure the segment opposite of the angle and the hypotenuse.
sin = opposite/hypotenuse

you won't be very accurate however, but it will give you a rough estimate

***just use a calculator...if you left it at school, there is a wonderful scientific calc built into your computer...open the normal calculator, view>>>>scientific and degrees

Answer 2

I assume you mean sin 20°, since if it's 20 radians there's no chance at all.

sin (3A) = 3 sin A - 4 sin^3 A

So if x = sin 20°, we get
√3 / 2 = sin (60°) = 3x - 4x^3
<=> 4x^3 - 3x + √3 / 2 = 0

If you solve this cubic equation, the answers will be sin 20°, sin 40°, and sin 260°. However, I don't think you're going to have much luck finding exact solutions for this (except in terms of sin 20°, etc.)

Answer 3

No; the only integer values you can compute the sines of exactly are those that are multiples of 3. You can compute sin (3), sin (6), sin (9), sin (12), and so on, exactly using trigonometric identities, but not sin (20), because 20 isn't a multiple of 3.

It is, of course, possible to approximate its value. The answerer above me gives one method of doing so.

Answer 4

You can use the following infinite series to find sin(20º):
∞
Σ [x^(2x+1)]/(2x+1)! = sin (x rad.)
0

Mutiply 180/π to convert from radians to degrees.

Answer 5

the book of law of sins. its hugeeeee
just use a calculator