L30 - Lecture 30 Section 4.7 Inverse Trigonometric...

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Unformatted text preview: Lecture 30: Section 4.7 Inverse Trigonometric Functions The Inverse Sine Function 1 π- π-1 Let’s restrict the domain to the interval uni005B.alt02 − u1D70B 2 , u1D70B 2 uni005D.alt02 . Then u1D466 = sin u1D465 is one-to-one. Def. The inverse sine function is defined by u1D466 = sin − 1 u1D465 if and only if with domain [ − 1 , 1] and range uni005B.alt02 − u1D70B 2 , u1D70B 2 uni005D.alt02 . NOTE: The inverse sine function is also called arcsine , denoted by u1D466 = arcsin u1D465 . ex. Find the exact value, if possible. 1) sin − 1 uni0028.alt03 1 2 uni0029.alt03 2) sin − 1 uni0028.alt04 − √ 3 2 uni0029.alt04 3) sin − 1 uni0028.alt03 3 2 uni0029.alt03 ex. Graph u1D466 = arcsin u1D465 2 2 π π-1 1 2--- 2-- π π 1-1 The Inverse Cosine Function π- 1- 1 π Restrict the domain to the interval [0 , u1D70B ]: Def. The inverse cosine function (or arccosin function , denoted by u1D466 = arccos u1D465 ) is defined by u1D466 = cos − 1 u1D465 if and only if with domain [ − 1 , 1] and range [0 , u1D70B ]....
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L30 - Lecture 30 Section 4.7 Inverse Trigonometric...

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