How do you use a linear approximation or differentials to estimate #tan44º#?

Answer 1

#~~ 0.965#

The derivative of #tan theta# is #sec^2 theta#, so that to a first order in #delta theta# we have
#tan(theta - delta theta) = tan(theta) -sec^2 theta xx delta theta#
To estimate #tan 44^circ# we must use #theta = pi/4# and #delta theta = pi/180# (remember that in calculus angles must be measured in radians) so that
#tan 44^circ ~~ tan (pi/4)-sec^2 (pi/4) xx pi/180 = 1-2 xx pi/180 ~~ 0.965#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To estimate ( \tan(44^\circ) ) using linear approximation or differentials, you can use the fact that for small angles, the tangent function is approximately equal to the angle itself measured in radians.

Since ( 44^\circ ) is not very large, we can use the linear approximation:

( \tan(x) \approx x ) for small ( x ) in radians.

Converting ( 44^\circ ) to radians:

( 44^\circ \times \left( \frac{\pi}{180} \right) = \frac{44\pi}{180} ) radians.

Thus, ( \tan(44^\circ) \approx \frac{44\pi}{180} ).

You can then calculate the numerical value using this approximation.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7