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death2833
14.10.2019 •
Mathematics
The parametric equations of a curve are x=e^-t*cost y=e^-t*sint show that dy/dx=tan(t-pi/4)
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Ответ:
Using product rule: f'g + fg'
Factor out
Next, we have to use trig identities to equate this with tan(t - pi/4).
There are a lot of steps here, i think its easiest to start at either end and meet in the middle. I will show that:
Starting on left side, use angle sum identity for tan. Note tan(pi/4) = 1.
Now starting on right side:
Therefore proving that
Ответ: