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Inverse Tangent Functions

Inverse Tangent Functions. Lesson 5.6. Remember… y = tan x. y = tan -1 x. If we took y = tan x on its entire domain, the inverse would not be a function So, we restrict the domain of tan -1 x to – π /2 ≤ y ≤ π /2 Different calculators  tan -1 x = arctan = atan.

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Inverse Tangent Functions

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  1. Inverse Tangent Functions Lesson 5.6

  2. Remember… y = tan x

  3. y = tan-1 x • If we took y = tan x on its entire domain, the inverse would not be a function • So, we restrict the domain of tan-1x to –π/2 ≤ y ≤π/2 Different calculators  tan-1 x = arctan= atan

  4. Remember… y = tan x • Lorem

  5. y = tan-1 x • Lorem

  6. Example 1 • Evaluate Arctan 30 to the nearest thousandth of a degree. • tan x = 30 • x = 88.09˚

  7. Example 2 • Evaluate tan-1 in radians • tan x = • x = arctan • x = 30˚ so π/6

  8. Example 3 • Give the angle θ the line y = mx makes with the positive part of the x – axis as a function of the slope of the line. Tan θ = m m θ = atan m θ 1

  9. Homework Pages 342 – 343 4 – 12, 14 – 15, 17 - 18

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