Radians and degrees

[[[((Background info on me...))  I love math...and I'm old :) haha! Some things that are taught regularly nowadays in math I did not learn in HS or College...I took calculus in college from a prof who didn't explain it in ways that I could understand, and that flat-out turned me off to calculus and higher maths.  Now my high school son is taking calculus...and I'm the homeschool mom...so I'm doing the class right along with (well a little ahead of!) him...we'll see how this goes!  ]]]

Last year my son took pre-calc at the community college and had trouble with radians and related work. I didn't have any clue, so I could not really help him too much...but now I've learned what they are and it's so easy!!

What is a radian? Basically pi radians = 180 degrees.  So to transform between degrees and radians, you just use the fraction 180°/π radians  or π radians/180°

so for example, if you would like to see how many radians is 74° ?

well, 74° * π radians/180°, so that'd give you 1.2915 radians

hmmm....

well, applying all of that to geometry/trigonometry type stuff...

you will see that 30° equals π/6 and 60° equals π/3 and 45 ° equals π/4   and then you can use your triangle rules for a 30-60-90 triangle proportions, where the side opposite the 30 would be 1, the side opposite the 60 is √3 and the hypotenuse is then 2.  You can easily do the sines/cosines/tangents etc using this triangle.  And for the 45-45-90 triangle you can use the π/4 relationship as well:

and then you can use the sin/cos/tan/cot/sec/csc functions with it...

Yeah, anyhow, I'm pretty excited about that hahaha!  Yes, I can see the humor in the fact that I'm liking this and I know not everyone likes math, but frankly it's pretty fun for me...so I'm glad to understand this part now! 

:)