How to find the approximate value of the differential of COS 30 degree * 12 in higher numbers?

How to find the approximate value of the differential of COS 30 degree * 12 in higher numbers?

Is it 30 ° 12 '= cos (π / 6 + π / 900) ≈ cos (π / 6) - sin (π / 6) * (π / 900) = √ 3 / 2 - π / 1800 ≈ 0.86428cos30.12 ° = cos (π / 6 + π / 1500) ≈ cos (π / 6) - sin (π / 6) * (π / 1500) = √ 3 / 2 - π / 3000 ≈ 0.86498

1) arctan 0.9

arctan0.9≈arctan1+[1/(1+1^2)]*(-0.1)
≈π/4-0.05
≈0.73539816339744830961566084581988

Find the inverse function of y = 2Sin (x + π / 4) (- 3 π / 4 ≤ x ≤ π / 4)

∵ -3π/4≤x≤π/4
∴ -π/2≤x+π/4≤π/2
∵ y=2sin(x+π/4)
∴ sin(x+π/4)=y/2
∴ x+π/4=arcsin(y/2)
∴ x=-π/4+arcsin(y/2)
The inverse function y = - π / 4 + arcsin (x / 2) (- 2 ≤ x ≤ 2)

Inverse function of y = 1 + 2Sin (1-x / 1 + x)

By y = 1 + 2Sin (1-x / 1 + x), there is a
(1-x)/(1+x)=arcsin(y-1)
1-x=arcsin(y-1)+x*arcsin(y-1)
(1+arcsin(y-1))*x=1-arcsin(y-1)
That is, the inverse function is: x = (1-arcsin (Y-1)) / (1 + arcsin (Y-1))

Y = 2Sin (1 / 2 + 3), X belongs to [2 / 2, 2 / 2] inverse function

X belongs to [2 / 2, 2 / 2] - > 1 x + 3 / 2 is in the second quadrant
-->x/2+pi/3=pi-arcsiny-->x=pi/3-2arcsiny-->
The inverse function is: y = pi / 3-2 arcsinx

Inverse function of y = 2 / X

x=2/y
If you still use y, then it's yourself

Find the inverse function y = 2 ^ x

Log y = x log 2 then y '= log (X-2)

The inverse function of y = 2 ^ x is

y=log(2)x

Find the inverse function of y = 3 ^ x (x > 2)

x> Then y = 3 ^ x > 9
y=3^x
Then x = log3 (y)
So the inverse function is y = log3 (x), x > 9

1、 27. The inverse function of y = 3 ^ X / (2 + 3 ^ x) is

y=3^x/(2+3^x)
2*y+y*3^x=3^x
3^x-y*3^x=2y
3^x(1-y)=2y
3^x=2y/(1-y)
lg3^x=x*lg3=lg[2y/(1-y)]
x=lg[2y/(1-y)]/lg3=log3 [2y/(1-y)]
So the inverse function is
y=log3 [2x/(1-x)] 0