Question

The approximate value of tan (44°30'), given that 1° = 0.0175^c, is ______.

Options

• 0.8952

• 0.9528

• 0.9285

• 0.9825

Answer 1

The approximate value of tan (44°30'), given that 1° = 0.0175^c, is 0.9825.

Explanation:

1° = 0.0175^c and tan (44°30')

Here, f(x) = tan x

f'(x) = sec²x

take 45 and h = `(1/2)^circ`

∴ h = `(-1/2)^\circ = 1/2 xx 0.0175`

= − 0.00875

and, f(a) = tan 45° = 1

f'(a) = sec² 45° = `(sqrt2)^2 = 2`

The formula for approximation is,

∴ f(a + h) = f(a) + h f'(a)

f(44°30') = `f(45^\circ) + (1/2)^\circ xx f'(45^\circ)`

= 1 + (−0.00875) × 2

= 1 − 0.0175

= 0.9825