Question

Find the approximate value of tan (44°) given $1^{\circ}=0.0175^{c}$

Answer 1

This can be solved by using "approximations", an application of derivatives.

It is important to have knowledge about derivatives and functions before solving  problem.

First, you need to keep this formula in your mind: f(a+h)  ≈ f(a) + h. f'(a). You may look up the proof for convenience

The problem: tan46=?

Now,

Step 1:

Let f(x) be your function.

Here, your function is tan(x). So,

f(x)=tan(x)

Step 2:

f'(x) --> derivative of f(x)

∴f'(x)= sec²x

Step 3:

Let 'a' be your number, rather the convinient number which is close to the standard angles.Here, it is 45, as tan(π/4)= 1

∴a=45°=π/4 radians.

Note: the angles need to be in radians and NOT in degrees for calculation.

Let 'h' be the remaining value to be added/subtracted (here added) to the 'a' to get the required number.

∴h=1° = 0.0175 radians

∴a+h= 46

Step 4:

Now, substituting values of 'a' , 'h' inplace of 'x' in f(x) in step 1.

f(a)=tanπ/4=1

f'(a)=sec²π/4= 2

f(a+h)= f[tan(45+1 )]= tan 46

Step 5:

Finally substituting all the values from step 3&4 in the formula:

f(a+h)≈f(a)+h.f'(a)

f(a+h)≈ 1+0.0175(2)≈ 1.035

Answer 2

Answer:

Step-by-step explanation:

using differentiate formula x is 45 and dx is -1 and solving this you will get0.96