Help finding the tangent line approximation to cosx at x=pi/4

Question

In class this morning we learned about linearization and I am still not confident in how it works but this is my attempt.

In part a of the question it asks to find the tangent line approximation to cosx at x=pi/4. I tried and got y=-√2 /2 x +((4+pi)(√2))/8

 

In part b it says to use a graph to explain how you know whether the tangent line approximation is an under or over estimate for 0≤x≤pi/2.

This I am unsure how to do. Does it refer to the first graph of the function or the approximation? I don't know but since it has a negative slope I would say it is decreasing? so I would assume it is an overestimate?

 

part c) to one decimal place, estimate the error in the approximation for 0≤x≤pi/2.

how do I find error? I know it's the little space between the point of the secant and tangent lines but I don't know how to calculate that.

Answer 1

You wrote: how do I find error? I no its the little space between the point of the secant and tangent lines but I don't know how to calculate that.

 

In the above excerpt, I've underlined two words that should have been know it's.

 

You find the error by simply taking the difference between actual value and the calculated estimate.

Since in the first quadrant the graph of cosine is concave downward, using the tangent will give overestimates.