Part 2/6:
Here, ( f'(a) ) represents the derivative of the function at the point ( a ), while ( f(a) ) denotes the function's value at that point. This formula allows engineers and mathematicians to approximate the value of a complex function with a simpler linear function when the variable is near a value ( a ).
Trigonometric Functions Near Zero
When considering small angles, particularly in radians, we can utilize linear approximation for trigonometric functions as follows:
Sine and Tangent
For both the sine and tangent functions, we observe that near zero:
( \sin(\theta) \approx \theta )
( \tan(\theta) \approx \theta )
These approximations stem from their derivatives: