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11. Inverse Trig functions

11. Inverse Trig functions. Inverse trig functions. sin -1 (x) cos -1 (x ) tan -1 (x) Can also be written arcsin (x), arccos (x), arctan (x). Inverse functions. If you remember from Math 2….. Functions must pass the horizontal line test in order for their inverse to be a function

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11. Inverse Trig functions

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  1. 11. Inverse Trig functions

  2. Inverse trig functions • sin-1(x) • cos-1(x) • tan-1(x) • Can also be written arcsin(x), arccos(x), arctan(x)

  3. Inverse functions • If you remember from Math 2….. • Functions must pass the horizontal line test in order for their inverse to be a function • Sin and cos do not pass the horizontal line test • Therefore we have to restrict their domain in order for their inverse to be a function

  4. arcsin • The part in bold is where we need to restrict its domain • So arcsin can only be between –π/2 and π/2 (the 1st and 4th quadrants)

  5. arccos • The part in bold is where we need to restrict its domain • So arccos can only be between 0 and π (the 1st and 2nd quadrants)

  6. arctan • We need to restrict the domain to just one piece of tangent • So arctanscan only be between - π /2and π/2 (the 1st and 4th quadrants)

  7. Take back out your unit circle!!!

  8. examples

  9. examples

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