Drawing the reference triangles for trig and inverse trig functions?

Question

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.) $csc^-1(-sqrt(2))$

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Answer 1 · 2018-03-14T00:36:37

$3$ 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) $arc csc (-sqrt2)= -pi/4$