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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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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)

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


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

  • sin–1 ½

  • sin–1 (–½)

  • sin–1 (3/2)


Inverse Cosine


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


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

  • cos–1

  • cos–1 (0)

  • cos–1 (5/7)


Inverse Tangent


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


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

  • tan–1 (1)

  • tan–1 ( )

  • tan–1 (-20)


Ex 4. Find the exact value of the expression, if it is defined.

a.)

b.)

c.)


Classwork:Book; pg. 557: 1,4,6,7,10,11,13,16,18,

21, 26,53,54


Classwork:Book; pg. 557: 1,4,6,7,10,11,13,16,18,

21, 26,53,54


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