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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.

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 defined:

Inverse Cosine (arccos) defined:

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 defined:

Inverse Tangent (arctan) defined:

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)

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

21, 26,53,54

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

21, 26,53,54

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