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Inverse Trig Functions

Inverse Trig Functions. 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?.

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Inverse Trig Functions

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  1. Inverse Trig Functions

  2. 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

  3. What do they look like? • These are the shift/2nd/function buttons on the 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)

  4. 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

  5. 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

  6. 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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