Advertisements
Advertisements
प्रश्न
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Advertisements
उत्तर
Let f(x) = sin x
Then f'(x) = `d/dx(sin x) = cos x`
Take a = 60° = `pi/(3) and h = 1°` = 0.0174c
Then f(a) = `f(pi/3)`
= `sin pi/(3)`
= `sqrt(3)/(2)`
= `(1.732)/(2)`
= 0.866
and
f'(a) = `f'(pi/3)`
= `cos pi/(3)`
= `(1)/(2)`
= 0.5
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ sin 61° = f(61°)
= `f(pi/3 + 0.0174)`
≑ `f(pi/3) + 0.0174.f'(pi/3)`
≑ 0.866 + 0.0174 x 0.5
≑ 0.866 + 0.00870
= 0.8747
∴ sin 61° ≑ 0.8747.
APPEARS IN
संबंधित प्रश्न
Find the approximate value of cos (60° 30').
(Given: 1° = 0.0175c, sin 60° = 0.8660)
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(25.3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(0.009)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(26)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(32.15)^(1/5)`
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%
If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area
If f (x) = 3x2 + 15x + 5, then the approximate value of f (3.02) is
A. 47.66
B. 57.66
C. 67.66
D. 77.66
The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is
A. 0.06 x3 m3
B. 0.6 x3 m3
C. 0.09 x3 m3
D. 0.9 x3 m3
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the loge 4.04, it being given that log104 = 0.6021 and log10e = 0.4343 ?
Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{26}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is
Find the approximate value of f(3.02), up to 2 places of decimal, where f(x) = 3x2 + 5x + 3.
Find the approximate values of : `sqrt(8.95)`
Find the approximate values of: `root(3)(28)`
Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`
Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.
Find the approximate values of : cot–1 (0.999)
Find the approximate values of : e0.995, given that e = 2.7183.
Find the approximate values of : loge(9.01), given that log 3 = 1.0986.
Solve the following : Find the approximate value of cos–1 (0.51), given π = 3.1416, `(2)/sqrt(3)` = 1.1547.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 is ______.
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
