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Question
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
Options
0.8952
0.9528
0.9285
0.9825
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Solution
The approximate value of tan (44°30'), given that 1° = 0.0175c, is 0.9825.
Explanation:
1° = 0.0175c 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
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