Inverse Trig

sin -1 = inverse sine
cos -1 = inverse cosine
tan -1 = inverse tangent

circular functions {arc cos, arc sin, and arc tan} arc is measured by the angel taht opens up to it.

Inverse undoes the function
x2 & Square root of x

multiplicative inverse = 3 times 1/3 = 1
additive inverse = 3 + -3 = 0

f(x) = x2
g(x) = square root of x
(f0g)(x) = (g0f)(x) = x
x is greater than or equal to zero.

Inverses

• reflections over y = x
  
• (x, y) - (y, x)


• (f0g)(x) = (g0f)(x) =x
  

To take an inverse you have to first restrict the domain

For inverses inputs and outputs switch.

Inverse Sine

y=sin(x)

Domain: (-3.14/2, 3.14/2)

Range: (-1, 1)

y=sin-1(x)


Domain: (-1, 1)


Range (-3.14/2, 3.14/2)

Inverse Cosine

y=cos(x)

Domain: (0, 3.14)

Range: (-1, 1)














y=cos-1(x)

Domain: (-1,1)

Range: (0, 3.14)

Inverse Tangent

y=tan(x)

Domain: (-3.14/2, 3.14/2)

Range: (-infinity, infinity)

y=tan-1(x)

Domain: (-infinity, infinity)

Range: (-3.14/2, 3.14/2)