# Thread: Divide a circle into 400 parts and call these measurements "Gradians"

1. ## Divide a circle into 400 parts and call these measurements "Gradians"

I am not having trouble with the division part. I need to know how to do the three trigonometric functions with gradians. Such as, sin(5)gradians = ? and cos(5)gradians = ? I don't really know where to begin to solve this.

2. ## Re: Divide a circle into 400 parts and call these measurements "Gradians"

Do you know how to do the trig functions in degrees? You know, I hope, that there are 360 degrees in a circle and, if you define a "gradian" to be 1/400 of circle there are 360/400= 0.9 degrees in a "gradian". The sine of 5 "gradians" is the sine of 5*.9= 4.5 degrees.

3. ## Re: Divide a circle into 400 parts and call these measurements "Gradians"

Isn't sine a y-coordinate? would I just times any of the units by 0.9 to get the y-coordinate? I don't fully understand how to get trig functions from anything but the common angles.

4. ## Re: Divide a circle into 400 parts and call these measurements "Gradians"

Also, how would I get cosine and tangent with these made up measurements?

5. ## Re: Divide a circle into 400 parts and call these measurements "Gradians"

There are 2 pi radians in a circle and 400 gradians in a circle, so $\displaystyle 2 \pi$ radians = 400 gradians. Hence to convert gradians to radians multiply by $\displaystyle 2 \pi/400 = \pi/200$ radians/gradian. Hence $\displaystyle \sin (5$ gradians) = $\displaystyle \sin (5 \times 2 \pi / 400$ radians) = $\displaystyle \sin (\pi/40$ radians).

Same thing with tangent and cosine - convert to radians then determine the values.

Alternatively, if you are more comfortable working in degrees then multiply the angle given in gradians by 0.9 to get the angle in degrees. But this is NOT the same thing as multiplying the value of the sine function by 0.9. In other words $\displaystyle \sin(0.9x) \ne 0.9 \sin(x)$

6. ## Re: Divide a circle into 400 parts and call these measurements "Gradians"

Originally Posted by nsganon101
Isn't sine a y-coordinate? would I just times any of the units by 0.9 to get the y-coordinate? I don't fully understand how to get trig functions from anything but the common angles.
Use a calculator!