CAS System Answer to Trigonometric Equation Query

[Starblazer]

Using the Ti-inSpire CAS I enter

Solve(sin (2x) = cos(2x),x)
(all in radians)

I get the answer
\(\displaystyle x = {(4 n15-3) \pi \over 8}\)

then if a re-run the command again I get
\(\displaystyle x = {(4 n16-3) \pi \over 8}\)

Please can you tell me what the n15 part is.

 

[HallsofIvy]

I have no idea what "TI-inspire" is (is the "TI" Texas Instruments"?) but to solve sin(2x)= cos(2x), let t= 2x so the equation becomes sin(t)= cos(t). The solutions to that are \(\displaystyle t= 2x= \pi/4+ k\pi\) where k can be any integer. From that \(\displaystyle x= \frac{\pi}{8}+ k\frac{\pi}{2}\). Combining fractions, that is \(\displaystyle x= \frac{(1+ 4k)\pi}{8}\). If we were to replace k by n- 1, which is also, of course, an arbitrary integer, that would be \(\displaystyle x= \frac{(1+ 4n- 4)\pi}{8}= \frac{(4n- 3)\pi}{8}\). But I have no idea what the "15" r "16" could mean. Have you considered reading the manual?

 

[Starblazer]

TI = Texas Instruments
Ti-nspire CX Cas = A calculator made by texas instruments.

If we were to replace k by n- 1, which is also, of course, an arbitrary integer, that would be [FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math]n[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main]) [/FONT][FONT=MathJax_Math]π /[/FONT][FONT=MathJax_Main] 8[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math]n[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Math]π/[/FONT][FONT=MathJax_Main] 8 [/FONT]. But I have no idea what the "15" r "16" could mean. Have you considered reading the manual?

I think n15, n16 is a label for n. I will look into by reading the manual.

Thank you

 

[HallsofIvy]

As a last resort, when nothing else works, read the manual!