2.  It must be one to one … pass the horizontal line test  Will a sine, cosine, or tangent function have an inverse?  Their inverses are defined over the following intervals:  Sine: [ -π/2, π/2 ]  Cosine: [ 0, π ]  Tangent: [ -π/2, π/2 ]

3.  y = sin -1 x or y = arcsin x  i.o.i sin y = x  y = cos -1 x or y = arccos x  y = tan -1 x or y = arctan x  Their graphs are on pg 324 if you would like to reference them

5.  1.) 2.)

6.  1.)  2.)  3.) It will be helpful to remember: sinθ = y then arcsin y = θ cos θ = x then arccos x = θ

7.  To do this on your calculator… ▪ 2 nd shift then trig function ▪ The steps are on page 325 if you need a refresher ▪ Let’s practice…. ▪ Pg. 328 #’s 2 – 26 even

8.  Pg. 328 #’s 1 – 41 odd

9.  Compositions of Functions  f (f -1 (x) ) = ?  f -1 ( f(x) ) = ?  Therefore:  sin(arcsin x) = xarcsin(sin y) = y  cos(arccos x) = xarccos(cos y) = y  tan(arctan x) = xarctan(tan y) = y  *remember - only works over certain intervals… ▪ Refer to page 326

10.  Use the co-terminal angles that are in the range!  Let’s practice:  1) arcsin[sin (π/2) ] = ?  2) arccos[cos (π/6) ] = ?  3) tan[arctan (-5)] = ?  4) arcsin[sin (-π/4)]= ?

11.  5) arcsin(sin 5π/3 ) = ? 6) sin(arcsin π ) = ?  7) arctan (tan π/6) = ? 8) tan(arcsin √2/2)=?  Pg. 328 #’s 44, 46, 48

12.  Ex. 1) Find the exact value of tan(arccos 2/3) ▪ Use a right triangle

13.  2.) sin(arccos √5/ 5) 3.) csc[arctan(-5/12)]

14.  Ex.1) sin(arccos 3x) ; 0 ≤ x ≤ 1/3  Ex 2) cot(arcsin 2x) ; 0 ≤ x ≤ 1/3  Practice pg. 328 #’s 60, 64, 66, 68

15.  Pg. 328 #’s 47-73 odd, 91, 95