Use linearization to approximate tan 59

Question

Would you use radians for this or a calculator? Im very lost. How do we apply the formula?

Answer 1

We know that tan(60°) = √3 and we want to know tan(59°), which is 1 degree less than 60° by linearizing the tangent function around x₀ = 60° = π/3.

 

 

In other words, we want to write a line tangent to f(x) = tan(x) through the point (π/3, √3) and use that to approximate the value of tan(59°).  Yes, do convert 59° into radians.

 

 

A. Find the derivative of tan(x) and evaluate it at π/3.  This is the value of the slope of your line.

 

B. Use the slope in A and (π/3, √3) to write the equation of the line tangent to tan(x).

 

C. Use the line to approximate the value of tan(59°).  [Convert degrees into radians.] 

 

D. Check the answer by calculating tan(59°) using a calculator.  The answer from the linearization should be within 1% of the actual value.

 

 

Good luck!