Inverse Trig Functions

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What do they do?
 These are the way we can undo a trig function
 Just like we subtract to undo adding
 Divide to undo multiplication
 Take the root to undo an exponent
 Raise by the base to undo a log
What do they look like?
 These are the shift/2nd/function buttons on the
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sin/cos/tan buttons
sin-1(y/r) = angle
cos-1(x/r) = angle
tan-1(y/x) = angle
So you input the ratio, and it outputs an angle
(unlike the sin(), cos(), and tan(), where you input
angles and they output ratios)
Let’s use them then
 sin-1(1/2) = angle
 cos-1(1) = angle
 tan-1(1) = angle
 sin-1(√(3)/2) = angle
 cos-1(- √(3)/2) = angle
 tan-1(0) = angle
How to write the answer
 As you hopefully noticed in doing the examples, these
inverse functions get more than one answer
 So, we write the answer in a way to account for that,
using +360n or +2πn for sin or cos, and +180n or + πn
 EG: sin-1(1/2)
= 30 + 360n
 or
= π/6 + 2πn
What if it’s csc, sec, cot?
 Solve for the ratio; for csc, for example, set the thing in
parenthesis equal to the ratio r/y; since r is always 1,
you can solve easily by cross multiplication.
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