Level 453 Level 455
Level 454

Inverse Trigonometric Functions


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sin^-1x = y
sin y = x same for cos,tan,csc,sec,cot
sin^-1(sinx)
x for (-pie/2 <= x <= pie/2)
sin(sin^-1x)
x for (-1<=x<=1)
d/dx(sin^-1x)
1/sqrt(1-x^2)
d/dx(cos^-1x)
-1/sqrt(1-x^2)
d/dx(tan^-1x)
1/1+x^2
pie/2
lim tan^-1x and x approaches xfinity
-pie/2
lim tan^-1x and x approaches -xfinity
d/dx(csc^-1x)
-1/x*sqrt(1-x^2)
d/dx(sec^-1x)
1/x*sqrt(1-x^2)
d/dx(cot^-1x)
-1/1+x^2
d/dx(sin⁻¹x)
1/√1-x²
d/dx(cos⁻¹x)
-1/√1-x²
d/dx(tan⁻¹x)
1/1+x²
d/dx(csc⁻¹x)
-1/x√x²-1
d/dx(sec⁻¹x)
1/x√x²-1
d/dx(cot⁻¹x)
-1/1+x²