MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C97CE5.3EFB6E70" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions

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The Inv= erse Trigonometric Functions
Ó=  <= /span>= Fra= nk Ma 2= 006
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Suppose we know cos(q) =3D 1, what is q?
        = ;            &n= bsp;  
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Suppose we know cos(q) =3D 1, what is q?
Actually, there are infinitely many possible
answers: q =3D 0, ±2π, ±= 4π, ±= 6π, …
        = ;            &n= bsp;
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Suppose we know cos(q) =3D 1, what is q?
Actually, there are infinitely many possible
answers: q =3D 0, ±2π, ±= 4π, ±= 6π, …
To make this inverse procedure into a function, = we designate q =3D 0 as the &#= 13;
        = ;   "cosine inverse of 1= "
        = ;            &n= bsp; 
Ó=  <= /span>= Fra= nk Ma 2= 006
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Suppose we know cos(q) =3D 1, what is q?
Actually, there are infinitely many possible
answers: q =3D 0, ±2π, ±= 4π, ±= 6π, …
To make this inverse procedure into a function, = we designate q =3D 0 as the &#= 13;
        = ;   "cosine inverse of 1= "
and its written as
        = ;   cos-1(1) =3D 0 =3D q.         = ;            &n= bsp;   
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0130.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
In general, let a be a number such that -1< a <1 = , there are infinitely many q such that cos(q) =3D a.
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0130_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 AAEAgAAAAAAAAAIJjI8Iy+3vkjwFADs= ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0143.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
In general, let a be a number such that -1< a <1 = , there are infinitely many q such that cos(q) =3D a.
However, there is exactly one q between 0 and <= /span>π such that cos(q) =3D a.
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0143_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 AAEAgAAAAAAAAAIJjI8Iy+3vkjwFADs= ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0144.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
In general, let a be a number such that -1< a <1 = , there are infinitely many q such that cos(q) =3D a.
However, there is exactly one q between 0 and <= /span>π such that cos(q) =3D a.
We designate this q where 0 < q < π, as the
        = ;   "cosine inverse of a= "
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0144_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 AAEAgAAAAAAAAAIJjI8Iy+3vkjwFADs= ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0144_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 AAIAgAAAAACAAAIOjI8Iy+3vkpzUwItXTQUAOw== ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0145.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
In general, let a be a number such that -1< a <1 = , there are infinitely many q such that cos(q) =3D a.
However, there is exactly one q between 0 and <= /span>π such that cos(q) =3D a.
We designate this q where 0 < q < π, as the
        = ;   "cosine inverse of a= "
and its written as
        = ;   cos-1(a) =3D  q ( given that        = ;     )
-1 &l= t; a < 1
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0145_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 AAEAgAAAAAAAAAIJjI8Iy+3vkjwFADs= ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0145_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 AAIAgAAAAACAAAIOjI8Iy+3vkpzUwItXTQUAOw== ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0145_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAIAgAAAAAAAAAINjI8Hy+0Pkpw0wAtrKgA7 ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example: The angles q where cos(q) =3D ½ are
q =3D ±π/3, ±= π/3±= 2π, ±= π/3±= 4π, …<= span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil= y: "Times New Roman";mso-hansi-font-family:"Times New Roman"'>
1/2
1
π/3±2n= π
Ó=  <= /span>= Fra= nk Ma 2= 006
-π<= /span>/3±2nπ
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AF+oi22iIiIIiICIiCLkb0IwHs2n8NqtIiAiIgIiICIiAiIgz0FIKCghpGvLxC0NDiLErQiICIiA iIgIiICIiD//0v7KiIg//9k= ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example: The angles q where cos(q) =3D ½ are
q =3D ±π/3, ±= π/3±= 2π, ±= π/3±= 4π, …<= span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil= y: "Times New Roman";mso-hansi-font-family:"Times New Roman"'>
π/3 is the angle between&= #13;
0 and π such that cos(= π/3)=3D½= , <= /div>
hence cos-1(½= ) =3D π/3.
1/2
1
π/3±2n= π
-π<= /span>/3±2nπ
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charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example: The angles q where cos(q) =3D ½ are
q =3D ±π/3, ±= π/3±= 2π, ±= π/3±= 4π, …<= span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil= y: "Times New Roman";mso-hansi-font-family:"Times New Roman"'>
π/3 is the angle between&= #13;
0 and π such that cos(= π/3)=3D½= , <= /div>
hence cos-1(½= ) =3D π/3.
1/2
1
Example: Using calculator,
cos-1(0.8) » 36.9o         = ;  cos-1(0.4) »66.4o&#= 13;
cos-1(0.2) » 78.5o         = ;  cos-1(-0.3) <= span style=3D'font-family:Symbol;mso-ascii-font-family:Arial;mso-bidi-font-fami= ly: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:sy= mbol'>»107o
π/3±2n= π
-π<= /span>/3±2nπ
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The Inv= erse Trigonometric Functions
Example: The angles q where cos(q) =3D ½ are
q =3D ±π/3, ±= π/3±= 2π, ±= π/3±= 4π, …<= span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil= y: "Times New Roman";mso-hansi-font-family:"Times New Roman"'>
π/3 is the angle between&= #13;
0 and π such that cos(= π/3)=3D½= , <= /div>
hence cos-1(½= ) =3D π/3.
1/2
1
Example: Using calculator,
cos-1(0.8) » 36.9o         = ;  cos-1(0.4) »66.4o&#= 13;
cos-1(0.2) » 78.5o         = ;  cos-1(-0.3) <= span style=3D'font-family:Symbol;mso-ascii-font-family:Arial;mso-bidi-font-fami= ly: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:sy= mbol'>»107o
π/3±2n= π
-π<= /span>/3±2nπ
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R0lGODlhRAAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQBE ABsAgQAAAGb/ZoCAgAECAwJUjI+py+0fAJy0TmGztnj7r3Tg6InkWZno6qjsm7jwLM9vba94fu78 6Pt9gsINsZg5IlNLlrIJeUJb016VJL2GtKAs9+D9BgQAgOCMTqvX7Lb7DS8AADs= ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0125_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABE ABwAgQAAAGb/ZoCAgAECAwJVjI+py+0fAJy0TmmzrmL7v3Tg+InkaZno+qjsq7jwHMj0a99rrp98 P/oBS0OYsKg5IlPLXROlfEKiUge1yrhiY1tid6P9GsJiAQAgSKvX7Lb7DY/LCwA7 ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0125_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRQAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABE ABwAgQAAAGb/ZoCAgAECAwJVjI+py+0fAJy0TmmzrmL7v3Tg+InkaZno+qjsq7jwHMj0a99rrp98 P/oBS0OYsKg5IlPLXROlfEKiUge1yrhiY1tid6P9GsJiAUCATqvX7Lb7DY8LCgA7 ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example: The angles q where cos(q) =3D ½ are
q =3D ±π/3, ±= π/3±= 2π, ±= π/3±= 4π, …<= span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil= y: "Times New Roman";mso-hansi-font-family:"Times New Roman"'>
π/3 is the angle between&= #13;
0 and π such that cos(= π/3)=3D½= , <= /div>
hence cos-1(½= ) =3D π/3.
1/2
1
Example: Using calculator,
cos-1(0.8) » 36.9o         = ;  cos-1(0.4) »66.4o&#= 13;
cos-1(0.2) » 78.5o         = ;  cos-1(-0.3) <= span style=3D'font-family:Symbol;mso-ascii-font-family:Arial;mso-bidi-font-fami= ly: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:sy= mbol'>»107o
π/3±2n= π
-π<= /span>/3±2nπ
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R0lGODlhRAAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQBE ABwAgQAAAGb/ZoCAgAECAwJVjI+py+0fAJy0TmGztnj7r3Tg6InkWZno6qjsm7jwLM9vba94fu78 6Pt9gsINsZg5IlNLlrIJeUJb016VJL2GtKAs9+D9BsJfAQAgSKvX7Lb7DY/LCwA7 ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0126_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRQAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBE ABwAgQAAAGb/ZoCAgAECAwJVjI+py+0fAJy0TmGztnj7r3Tg6InkWZno6qjsm7jwLM9vba94fu78 6Pt9gsINsZg5IlNLlrIJeUJb016VJL2GtKAs9+D9BsJfAUCATqvX7Lb7DY8LCgA7 ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0127.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example: The angles q where cos(q) =3D ½ are
q =3D ±π/3, ±= π/3±= 2π, ±= π/3±= 4π, …<= span style=3D'font-family:Arial;mso-ascii-font-family:Arial;mso-bidi-font-famil= y: "Times New Roman";mso-hansi-font-family:"Times New Roman"'>
π/3 is the angle between&= #13;
0 and π such that cos(= π/3)=3D½= , <= /div>
hence cos-1(½= ) =3D π/3.
1/2
1
Example: Using calculator,
cos-1(0.8) » 36.9o         = ;  cos-1(0.4) »66.4o&#= 13;
cos-1(0.2) » 78.5o         = ;  cos-1(-0.3) <= span style=3D'font-family:Symbol;mso-ascii-font-family:Arial;mso-bidi-font-fami= ly: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:sy= mbol'>»107o
Ó=  <= /span>= Fra= nk Ma 2= 006
π/3±2n= π
-π<= /span>/3±2nπ
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charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Summary of cos-1(a):
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Summary of cos-1(a):
• cos-1(a) is defined fo= r
1 &l= t; a= < 1
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The Inv= erse Trigonometric Functions
Summary of cos-1(a):
• cos-1(a) is defined for        = ;         
cos-1(a) =3D x , x is between 0 and π<= /span>
-1 &= lt; a= < 1
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The Inv= erse Trigonometric Functions
Summary of cos-1(a):
• cos-1(a) is defined for        = ;         
• cos-1(a) =3D q where        = ;          and cos(q) =3D a.
cos-1(a) =3D x , x is between 0 and π<= /span>
-1 &= lt; a= < 1
0 <= q = < π
(0o=  <= ; q < 1800)
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The Inv= erse Trigonometric Functions
Cos-1(a) is also call= ed arc-cosine of a  and written as arccos(a).
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Cos-1(a) is also call= ed arc-cosine of a  and written as arccos(a).
Example:
arccos(1) =3D 0 = ;
arccos(0) =3D π/2
arccos(-1/2) =3D 2π/3 = ;
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The Inv= erse Trigonometric Functions
Cos-1(a) is also call= ed arc-cosine of a  and written as arccos(a).
Example:
arccos(1) =3D 0 = ;
arccos(0) =3D π/2
arccos(-1/2) =3D 2π/3 = ;
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0096_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhTgA4AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABM ADYAgQAAAAAAAGb/ZgECAwLSlI+pyxgAo5y01oYzfrb7q4Ui95WeiGakyU7pu6ztDNeHPLO2jefl Xuv5TsCXcGgpGpEtZerIdDlHUdOUWv1cQ9AsYKvpZsEqL5HMEFfRDXWUnTZ34DF5kp5wM/F5eyUA GCg4SFhoKOiXqLjI2Oj4CBkpOUlZaXmJSXm4ydlpaBbAFwYqWuYVWtpGmhp3ytqahfra5zpLG2t7 WyWbK6D3wZv76xFsO9xRPHtskfy6/Nd7sxr9TNHMWj1xnZotsV3aHfEtGg4xzlcOcI6X7un+blgA ADs= ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Cos-1(a) is also call= ed arc-cosine of a  and written as arccos(a).
Example:
arccos(1) =3D 0 = ;
arccos(0) =3D π/2
arccos(-1/2) =3D 2π/3 = ;
Ó=  <= /span>= Fra= nk Ma 2= 006
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0097_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAy ABcAgQAAAAAAAGb/ZgECAwJDjI+py60Co5y02hsN3rxD7YXiF4xmB55qla4u+cZCK590Pd54qO9o 6TP1gpgh0WI8UpJKCbMJg3KeUGrTqnRot9xEAQA7 ------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0098.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Cos-1(a) is also call= ed arc-cosine of a  and written as arccos(a).
Example:
arccos(1) =3D 0 = ;
arccos(0) =3D π/2
arccos(-1/2) =3D 2π/3 = ;
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example:  Draw arccos(–3/4) and find = tan(arccos(–3/4)), no calculator.
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0147.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example:  Draw arccos(–3/4) and find = tan(arccos(–3/4)), no calculator.
        = ;            &n= bsp;            = ;            &n= bsp;            = ;     
=3Darccos(-3/4)
Set
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Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0148.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example:  Draw arccos(–3/4) and find = tan(arccos(–3/4)), no calculator.
        = ;            &n= bsp;           Find y using y2 + 9 =3D 16,
        = ;            &n= bsp;          
=3Darccos(-3/4)
Set
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The Inv= erse Trigonometric Functions
Example:  Draw arccos(–3/4) and find = tan(arccos(–3/4)), no calculator.
        = ;            &n= bsp;           Find y using y2 + 9 =3D 16,
        = ;            &n= bsp;           so y =3D &O= uml;7.
        = ;            &n= bsp;          
=3Darccos(-3/4)
Set
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The Inv= erse Trigonometric Functions
Example:  Draw arccos(–3/4) and find = tan(arccos(–3/4)), no calculator.
        = ;            &n= bsp;           Find y using y2 + 9 =3D 16,
        = ;            &n= bsp;           so y =3D &O= uml;7.
        = ;            &n= bsp;           Hence,
        = ;            &n= bsp;           tan(arccos(-3/4))
        = ;            &n= bsp;           =3D tan(q)
=3Darccos(-3/4)
Set
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The Inv= erse Trigonometric Functions
Example:  Draw arccos(–3/4) and find = tan(arccos(–3/4)), no calculator.
        = ;            &n= bsp;           Find y using y2 + 9 =3D 16,
        = ;            &n= bsp;           so y =3D &O= uml;7.
        = ;            &n= bsp;           Hence,
        = ;            &n= bsp;           tan(arccos(-3/4))
        = ;            &n= bsp;           =3D tan(q) =3D -Ö7 /3=
=3Darccos(-3/4)
Set
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The Inv= erse Trigonometric Functions
Example:  Find arccos(cos(-π<= /span>/3)), no calculator. =
------=_NextPart_01C97CE5.3EFB6E70 Content-Location: file:///C:/4D764A33/14TheInverseTrigonometricFunctions_files/slide0158.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Inverse Trigonometric Functions
The Inv= erse Trigonometric Functions
Example:  Find arccos(cos(-π<= /span>/3)), no calculator. =
= ;
cos(-<= /span>π/3) = =3D ½,
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