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Question

Use differentials to approximate the value of tan (47) . Round your answer to the nearest thousandth. Hint: think in terms of radians

Answer 1

conversion from degrees to radians is x^° =πx/180 radians.

Note that 45 degrees =π/4 radians is a special angle, you should remember that its tangent value is 1

You can also determine the secant value by using the special triangle.

Set y(x) = tan x so a=π/4 and x=47π/180 (should see that x-a=δx=2π/180=π/90) and y'(x)= sec² x

y(47π/180) =y(π/4)+(π/90)sec²(π/4)