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Check Homework. PRE. Lesson 7.4: Inverse Trig Functions. Objectives: To define the inverse of the sine, cosine, and tangent functions. To understand the domain and range of the inverse trig functions. Inverse Sine. Inverse Sine (arcsin).

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PRE

Lesson 7.4: Inverse Trig Functions

  • Objectives:
  • To define the inverse of the sine, cosine, and tangent functions.
  • To understand the domain and range of the inverse trig functions.
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Inverse Sine (arcsin)

The inverse of the function sin is the function sin–1 defined by: for –1 ≤ x ≤ 1 and –π/2 ≤ y ≤π/2.

sin y = x sin–1x = y

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Example 1. Find the exact value of the expression if it is defined:

  • sin–1 ½
  • sin–1 (–½)
  • sin–1 (3/2)
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Inverse Cosine (arccos)

The inverse cosine functionis the function cos–1with domain [–1, 1] and range [0, π], defined by:

cos y = x cos–1 x = y

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Example 2. Find the exact value of the expression if it is defined:

  • cos–1
  • cos–1 (0)
  • cos–1 (5/7)
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Inverse Tangent (arctan)

The inverse tangent functionis the function tan–1with domain and range (–π/2, π/2) defined by: tan y = x tan–1 x = y

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Example 3. Find the exact value of the expression if it is defined:

  • tan–1 (1)
  • tan–1 ( )
  • tan–1 (-20)
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