Integration cos pi fuction help (deg or rad)?

Question

Hi,
can you please help me?
As a HW assignment we needed to integrate:

cos(3x + 4) dx.....with borders from 0 to pi.(3,14)
1st step: substitute 3x+4 with u.
u=3x+4
du/dx= 3
dx= 1/3du

And change borders: u(0)= 3.0 +4= 4
u(pi)= 3.pi+4

So now our function to integrate is:

cos u 1/3du.....with borders from 4 to 3pi+4
=
1/3[sin u]...borders from 4 to 3pi+4

So now comes my problem and question:

I had my calculator on degrees and got: 1/3(0,232-0,07)= 0,05 as answer

However the answer should be:
1/3(0,757--0,757)= 1/3(1,514)=0.504
Which is what you get when putting the calculator on radians

So My question(Finally)
How should you know whether the calculator should be set to radians or degrees

Bent Snowman · Accepted Answer

"So My question(Finally)
How should you know whether the calculator should be set to radians or degrees"

Could have started with this after you gave us the integral, no need to show us your solution. 

You know if a function is talking about radians or degrees by context, but you should assume it is in radians unless told otherwise. Here, integrating from 0 to pi only makes sense from a "creating a problem" standpoint if you were doing radians, no one talks about pi degrees, it is silly.

If you are unsure, ask your teacher, but you need to develop a sureness in your own judgment as well. Here, it should be (someday) "obvious" to you that this surely must have been in radians. People make problems and they try to make them "clean" in the respect that the numbers work out well. Here, using pi and 0 is "clean" because those are exact values when you are talking about radians that everyone knows the values of trigonometric functions for. Know what I mean?

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Integration cos pi fuction help (deg or rad)?

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