Through out my studies, I had been through a lot of trigonometry and differential equations with trigonometry. Whenever 'pi' appears inside the sin/cos/tan..etc, I assumed it to be 180, and when it appeared outside due to integration or something else, I assumed it to be the irrational number-3.14, sometimes, both at a time. I read a lot about radians and degrees. But Most math problems don't specify if it's radians or degrees. Is it implied that whenever pi appears inside the trigonometric functions it is in degrees and outside in radians? or the other way round? Sorry I'm totally confused. I just wanna have some clarity. Also, calculators seem to take the same 'pi' value inside and outside which is causing ridiculous errors. like sin 180 coming out as sin 22/7*. Please help.
Please give an example: say this: So, if there is an integral which, say x*sin(x), integrated over 0 and pi/5., After the integration is over, how do you apply the limits? Do you use pi=180 inside the -cos and the irrational just number on the plain old x?