Question

How do you find the linear approximation of tan(3 degrees) using differentials?

Answer 1

\[3 ^{\circ}=\frac{3 \cdot \pi}{180}= \frac{\pi}{60} \\ \text{ I would find the tangent line to } f(x)=\tan(x) \text{ at } x=0 \text{ since } \frac{\pi}{60} \text{ is pretty close to zero }\]

Answer 2

so it would be 3-0 then?

Answer 3

to zero <--got cut off at that bit

Answer 4

3-0? what does that mean?

Answer 5

the \[\Delta x\]

Answer 6

the tangent line to f at x=a is
\[y=f'(a)(x-a)+f(a)\]
which we will use as an approximation for f
\[f(x) \approx f'(a)(x-a)+f(a) \text{ for values close to } x=a\]

Answer 7

thank you!