How do I find the radian version of tan 34.22 (tan60=root 3 for example)?

Question

I'm trying to answer this problem and I need to figure out how to translate tan 34.22 into a root (such as tan60 = Root of 3). How would I go about doing this?

Answer 1

I think you're confused. You say that you need to find the radian version of a degree angle that's evaluated in the tangent function. No matter what you use, degree angle measurement or radian angle measurement, they will produce the same answer when evaluated, one after the other, in any of the six trig. functions. For example, tan(60)=root3 and tan(pi/3)=root 3. It doesn't matter which measure you use, they will always produce the same answer. As far as translating something into a root, good luck. If you take the square root of 3 on a calculator or by hand, you will always end up with a decimal (unless using a fancy graphing calculator or software), and further, in mathematics it's always best to simplify as far as you can. Therefore, root 3 will do in tan(60) and not the decimal version, because in later math, you'll find situations where that same root 3 will be used again or be helpful to simplify the same problem you're working on at the time. I hope you post a more specific question on what you're trying to ask here.

P.S. You're working in decimal degrees, too. So, when you convert it to radians, with the conversion factor pi/180, you'll find that you get approximately pi/5.26.... If I were you, I would stick to decimal degrees and evaluate through the tan function.

By the way, to convert decimal degrees to degrees, minutes, seconds, use your knowledge of time:
34 degrees, .22 x 60minutes/1degree = 13.2,
.2 x 60seconds/1minute = 12 So 34.22 in dms is 34 deg 13 min 12 sec

Reverse to decimal degrees:34 + 13min x 1degree/60min. = 34.2166 + 12sec x 1degree/3600sec = .00333. Is approximately 34.22 degrees. There you go!

Answer 2

I'm confused as to what you're really asking. you ask for the radian version. To change degrees to radians, you multiply the angle (in degrees) by (π radians / 180º). So 60º becomes 60º * (π/180º) = π/3 radians. That's really the only conversions I know of for angles.

The example you use (tan60=√( 3)). Here you're relating a function of the angle (tangent) to the lengths of the associated sides of a right triangle
(side opposite the angle / side adjacent to the angle) = (sin ø / cos ø).

Just mucking around on my calculator, I don't see anything special about the angle 34.22º or 34.22 radians. Maybe you can restate your question by adding information?

Answer 3

tan(34.22 radians) ≈
tan(0.8925643π radians) ≈
- (1/5)√3 ≈ - (1/7)√6 ≈ - √42/341 ≈ -0.3509481
All of these are approximations.