Drawing the reference triangles for trig and inverse trig functions?

I understand which quadrants house each positive function, but am unsure how you determine the quadrant that these functions go in.
ex-
1.) #sin^-1(1)#

2.) #tan^-1(-1)#

3.)#sec^-1(1/2)#

4.) #csc^-1(-sqrt(2))#

1 Answer
Mar 14, 2018

#3# rules:

  • #(1)# Know that #cos#, #sec# functions are restricted to quad #1# and #2#
  • #(2)# Know that #tan#, #cot#, #sin#, #csc# are restricted to quad #1# and #4#
  • #(3)# And when you go to quadrant #4# with #tan#, #cot#, #sin#, #csc#, use negative angles

1) #arcsin(1)= pi/2#
2) #arctan(-1)= -pi/4#
3) #arcsec(1/2)= DNE#
4) #arc csc (-sqrt2)= -pi/4#