What are arcsin, arccos and arctan?

• These functions are the?inverse functions?of?sin,?cos?and?tan
  • sin?(arcsin?x)?=?x
  • cos?(arccos?x)?=?x
  • tan?(arctan?x)?=?x
• The domains of?sin,?cos, and?tan?must first be restricted to make them one-to-one functions (only one-to-one functions have inverses)

What are the restricted domains?

• domain of?sin?x?is restricted to?-π/2?≤?x?≤?π/2??(-90°?≤?x?≤?90°)

• domain of?cos?x?is restricted to?0?≤?x?≤?π??(0°?≤?x?≤?180°)

• domain of?tan?x?is restricted to?-π/2?<?x?<?π/2??(-90°?<?x?<?90°)

What does the graph of arcsin look like?

• The graph of?y?= arcsin?x?looks like this:

• the?domain?is?-1?≤?x?≤ 1
• the?range?is?-π/2?≤?arcsin?x≤?π/2??(-90°?≤?arcsin?x?≤?90°)

What does the graph of arccos look like?

• The graph of?y?= arccos?x?looks like this:

• ?the?domain?is?-1?≤?x?≤ 1
• the?range?is?0?≤?arccos?x?≤?π??(0°?≤?arccos?x?≤?180°)

What does the graph of arctan look like?

• The graph of?y?= arctan?x?looks like this:

• the?domain?is?x?∈??? (ie arctan?x?is defined for?all?real number values of?x)
• the?range?is?-π/2?<?arctan?x?<?π/2??(-90°?<?arctan?x?<?90°)
• horizontal?asymptotes?at?y=?-?π/2?and?y?=?-π/2