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Aim: How do we differentiate Inverse Trig functions?

Aim: How do we differentiate Inverse Trig functions?. Do Now:. Does y = sin x have an inverse?. yes, but only in restricted domain. Definition of Inverse Trig Functions. alternate notation. arcsin x  sin -1 x. ‘the angle whose sin is . . .’. Graphs of Inverse Trig Functions.

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Aim: How do we differentiate Inverse Trig functions?

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  1. Aim: How do we differentiate Inverse Trig functions? Do Now: Does y = sin x have an inverse? yes, but only in restricted domain.

  2. Definition of Inverse Trig Functions alternate notation arcsinx  sin-1 x ‘the angle whose sin is . . .’

  3. Graphs of Inverse Trig Functions

  4. Graphs of Inverse Trig Functions y = arccsc x y = arcsec x y = arctan x

  5. 1 0 UND. 1 however, restricted domain Evaluating Inverse Trig Functions ‘the angle whose sin is -1/2’ reference angle of /6 sin is negative in QIII and IV angle y is - /6

  6. 1 0 UND. 1 however, restricted domain Evaluating Inverse Trig Functions ‘the angle whose cos is 0’ reference angle of /2 angle y is /2

  7. 1 ‘the angle whose tan is ’ 0 UND. 1 however, restricted domain Evaluating Inverse Trig Functions reference angle of /3 angle y is /3

  8. Using Inverses to Solve an Equation take tan of both sides inverse property x = 2 solve for x

  9. Using Right Triangles Given y = arcsin x, where 0 < y < /2, find cos y. Since y = arcsin x, then sin y = x 1 x opposite y

  10. Using Right Triangles Since y = arcsec x, then sec y = x opposite 1 y 2 adjacent

  11. Derivatives: Inverse Trig Functions derivative of inverse sine

  12. Derivatives of Inverse Trig Functions

  13. Model Problems u = 2x u = 3x u = x1/2 u = e2x

  14. Model Problems u = x2 u = 5x u = x2 - x

  15. Algebraic Transcendental Logarithmic Exponential Trigonometric Inverse Trigonometric Polynomial Rational Functions w/radicals Elementary Functions Elementary functions have proven sufficient to model most phenomena in physics, chemistry, biology, engineering, economics, etc. An elementary function is a function from the following list or one that can be formed as a sum, product, quotient or composition of functions in the list.

  16. 1 0 UND. 1 Using Right Triangles

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