How to graph Fourier Transform

[onyx osprey]

I'm having trouble graphing the frequency domain representation of f(t) = sin(10πt).
I'm not entirely sure how F(e^iω0t) = 2πδ(ω-ω0) works, or where the -i comes into play with the graph.

I'm currently making a presentation for year 12 ext 2 maths. I'm working on the use of further integration to solve difficult problems, and for some reason I've focused on the use of the fourier transform.

I'd really appreciate it if someone could help me 😭 🙏

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[shrewd tiger]

@onyx osprey

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[shrewd tiger]

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Feb 17, 2025, 4:21 AM

[deep siren]

sin(x) = (exp(ix) + exp(-ix))/2i

As you already mention

Overall I think your work is sound

But since your function is pure imaginary valued

You can just graph the imaginary part