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Question
The approximate value of tan (44° 30°), given that 1° = 0.0175, is ______.
Options
0.8952
0.9528
0.9285
0.9825
Solution
The approximate value of tan (44° 30°), given that 1° = 0.0175, is 0.9825.
Explanation:
I° = 0.0175 and tan (44° 30°)
Here, f(x) = tan x
f'(x) = sec2x
take 45 and h = `(1/2)^°`
∴ h = `(-1/2)^° = 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°) + `(1/2)^° xx f'(45°)`
= 1 + (-0.00875) × 2
= 1 − 0.0175
= 0.9825
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