I'm trying to calculate a sine wave using the formula... $$ x(t) = A\sin{(2 \cdot \pi \cdot f_q \cdot t)} $$ Where $t$ is time (seconds), $A$ is amplitude and $f_q$ is frequency (Hz)
When I calculate $x(1) = 1 \cdot \sin{(2 \cdot \pi \cdot 1 \cdot 0.25)}$, I get $1$ which is expected. However, when I calculate $x(1) = 1 \cdot \sin(2 \cdot \pi \cdot 20000 \cdot 1)$, I get -1.9427294e-12. How is the answer $\gt -1$?...The amplitude is 1.
Thanks in advance...
Your equation of
$$x(t) = A\sin(2\pi \times f_q \times t) \tag{1}\label{eq1}$$
has an amplitude of $|A|$, so with $A = 1$, it's amplitude is $1$, as you state. This means the range of the possible values is $-1 \le x(t) \le 1$. With the second set of calculations where you get
$$x(1) = 1 \times \sin(2\pi \times 20000 \times 1) = -1.942794\text{e-}12 \tag{2}\label{eq2}$$
the value of $-1.942794\text{e-}12$ is in scientific notation and means $-1.942794 \times 10^{-12}$, i.e., it is $-0.000000000001942794$, which is very close to the correct value of $0$. Also, this is $\gt -1$, as you state, so it's a valid value.