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DO NOW:

DO NOW:. Evaluate: sin -1 (1/2) cos -1 (1/2) tan -1 (1). 3.8 – Derivatives of Inverse Trigonometric Functions. HW: Pg. 170 #2 - 8e, 14 - 26e. Inverse Trigonometric Functions. Apply implicit differentiation to find the derivatives of the inverse trigonometric functions.

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DO NOW:

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  1. DO NOW: • Evaluate: • sin-1(1/2) • cos-1 (1/2) • tan-1 (1)

  2. 3.8 – Derivatives of Inverse Trigonometric Functions HW: Pg. 170 #2 - 8e, 14 - 26e

  3. Inverse Trigonometric Functions • Apply implicit differentiation to find the derivatives of the inverse trigonometric functions. y = sin-1x means siny = x and

  4. Inverse Trigonometric Functions • This leads to the following formula: • Try finding d/dx of tan-1x

  5. Find the derivative of y = cos-1x

  6. A particle moves along the x-axis so that its position at any time t ≥ 0 is x(t) = tan-1(√x) • What is the velocity of the particle when t = 16?

  7. Differentiate: (a) (b)

  8. Differentiate: • Y = sec-1x, |x|>1

  9. Let’s find the derivative of the arcsecant • y = sec-1x, |x| > 1

  10. Derivatives of the other three • Use the following identities: Inverse Function-Inverse Cofunction Identities • cos-1x = π/2 - sin-1x • cot-1x = π/2 - tan-1x • csc-1x = π/2 - sec-1x

  11. Calculator Conversion Identities • sec-1x = cos-1(1/x) • cot-1x = π/2 - tan-1x • csc-1x = sin-1(1/x)

  12. Find an equation for the line tangent to the graph of y = cot-1(x) • At x = -1

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