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5.8 Inverse Trig Functions

5.8 Inverse Trig Functions. Definition of Inverse Trig Functions. Graphs of inverse functions. Page 381. Ex. 1 Evaluating Inverse Trig Functions. a) arcsin (-1/2) b) arcsin (0.3). Properties of Inverse Functions. If -1≤x≤1 and – π /2≤y≤ π /2, then: sin( arcsin x)=x and arcsin (sin y)=y

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5.8 Inverse Trig Functions

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  1. 5.8 Inverse Trig Functions

  2. Definition of Inverse Trig Functions

  3. Graphs of inverse functions • Page 381

  4. Ex. 1 Evaluating Inverse Trig Functions • a)arcsin(-1/2) • b)arcsin(0.3)

  5. Properties of Inverse Functions • If -1≤x≤1 and –π/2≤y≤π/2, then: • sin(arcsin x)=x and arcsin(sin y)=y • If –π/2≤y≤π/2, then • tan(arctan x)=x and arctan(tan y)=y • If |x|≥1 and 0≤y≤π/2 or π/2≤y≤π, then • sec(arcsec x)=x and sec(arcsec y)=y • Similar properties hold true for the other trig functions

  6. Solving an Equation • arctan(2x – 3) = π/4

  7. Ex. 3 Use Right Triangles to Solve • Find cos(arcsin x), where 0≤y≤π/2

  8. Ex 3 cont…

  9. Ex 4 Write the expression in algebraic form • cos(arcsin 2x)

  10. Derivatives of Inverse Trig Functions

  11. Ex. 5 Find the derivative • a) • b)

  12. Ex 5. cont… • c) • d)

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