11. INVERSE TRIG FUNCTIONS

INVERSE TRIG FUNCTIONS

sin-1(x) cos-1(x) tan-1(x)

Can also be written arcsin(x), arccos(x), arctan(x)

INVERSE FUNCTIONS

If you remember from Math 2….. Functions must pass the horizontal line test in

order for their inverse to be a function Sin and cos do not pass the horizontal line test Therefore we have to restrict their domain in

order for their inverse to be a function

ARCSIN

The part in bold is where we need to restrict its domain

So arcsin can only be between –π/2 and π/2 (the 1st and 4th quadrants)

ARCCOS

The part in bold is where we need to restrict its domain

So arccos can only be between 0 and π (the 1st and 2nd quadrants)

ARCTAN

We need to restrict the domain to just one piece of tangent

So arctans can only be between - π /2 and π/2 (the 1st and 4th quadrants)

TAKE BACK OUT YOUR UNIT CIRCLE!!!

EXAMPLES

1 3sin

2

1 2cos

2

1tan 3

EXAMPLES1 3

cos(sin )2

1sin (cos315)

1tan(sin 1/ 2 )

1cos(tan 1 )

1tan(tan 3 / 3 )