Math 130 exam 2 (

Math 130 exam 2
-arctanx
-arctanx=y, tany=x and -π/2<y<π/2
-tan(arctanx)=x
-artan(tanx)≠x - ANS-Function f(x)=tanx
-name of the partial inverse associated with the interval
-graph of this partial inverse
-what the inverse means
-good cancellation law
-bad cancellation law

-arcsinx
-arcsinx=y means siny=x and -π/2≤y≤π/2
-sin(arcsinx)=x
-arcsin(sinx)≠x - ANS-function f(x)=sinx
-name partial inverse associated to that interval
-graph of partial inverse
-what that partial inverse means
-good cancellation law
-bad cancellation law

1/sinx - ANS-csc=

1/cscx - ANS-sinx=

1/cosx - ANS-secx=

1/secx - ANS-cosx=

1/tanx - ANS-cotx=(reciprocal identity)

t/cotx - ANS-tanx= (reciprocal identity)

sinx/cosx - ANS-tanx= (quotient identity)

cosx/sinx - ANS-cotx=(quotient identity)

1 - ANS-sin²x+cos²x=

1+tan²x - ANS-sec²x=

, 1+cot²x - ANS-csc²x=

-sinx - ANS-sin(-x)=

-cscx - ANS-csc(-x)=

cosx - ANS-cos(-x)=

sec x - ANS-sec(-x)=

-tanx - ANS-tan(-x)=

-cotx - ANS-cot(-x)=

cosx - ANS-sin(π/2-x)=

sinx - ANS-cos(π/2-x)=

0
π/6
π/4
π/3 - ANS-arctanx
x=0---->
x=1/√3-->
x=1------>
x=√3--->

0
π/6
π/4
π/3
π/2 - ANS-arcsinx
x=0---->
x=1/2-->
x=√2/2--->
x=√3/2--->
x=1

180 - ANS-π

360 - ANS-2π

90 - ANS-π/2