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More Examples on Inverse Trigonometric Functions and Formulas
Ó= ; 2006, Frank = Ma
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0040.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Definition of tan-1(a):
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0041.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Definition of tan-1(a):
• tan-1(a) is defined for all values a.        = ;        
Ó F= = r= a= = n= k<= span lang=3DEN-US style=3D'font-size:56%;color:red;mso-fareast-language:ZH-CN'>=  M= = a = 2= = 0= 0= 6
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Definition of tan-1(a):
• tan-1(a) is defined for all values a.        = ;        
• tan-1(a) =3D q where tan(q) = =3D a and        = ;      .
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More Examples on Inverse Trigonometric Functions and Formulas
Definition of tan-1(a):
• tan-1(a) is defined for all values a.        = ;        
• tan-1(a) =3D q where tan(q) = =3D a and        = ;      .
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More Examples on Inverse Trigonometric Functions and Formulas
Definition of tan-1(a):
• tan-1(a) is defined for all values a.        = ;        
• tan-1(a) =3D q where tan(q) = =3D a and        = ;      .
tan-1(a) =3D q
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Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Example A: Find cos(sin(-1/4) – tan(4)). Draw each angle.
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Example A: Find cos(sin(-1/4) – tan(4)). Draw each angle.
Let q=3Dsin-1(-1/4)        = ;            &n= bsp; 
Ó F= = r= a= = n= k<= span lang=3DEN-US style=3D'font-size:56%;color:red;mso-fareast-language:ZH-CN'>=  M= = a = 2= = 0= 0= 6
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0046.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Example A: Find cos(sin(-1/4) – tan(4)). Draw each angle.
Let q=3Dsin-1(-1/4)        = ;            &n= bsp; 
q=3Dsin-1(-1/4)
x
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Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0046_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhXAAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQBZ ABwAgAAAAABmAAJbTICpy+0Po3ymnomz3tAaDoYiZY3myXkXyraM6sayJ9csbOchrvca7QtOeMLi C2hMKpBKJbFZfEKF0mmvas1hs7YtN+b9tsLiG7NcI6NH6rWo7U6d4+YSfRYoAAA7 ------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Example A: Find cos(sin(-1/4) – tan(4)). Draw each angle.
Let q=3Dsin-1(-1/4)        = ;            &n= bsp; 
q=3Dsin-1(-1/4)
x=3DÖ15
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More Examples on Inverse Trigonometric Functions and Formulas
Example A: Find cos(sin(-1/4) – tan(4)). Draw each angle.
Let q=3Dsin-1(-1/4)        = ;            &n= bsp;  Let = α=3Dtan-1(4) =
q=3Dsin-1(-1/4)
x=3DÖ15
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More Examples on Inverse Trigonometric Functions and Formulas
Example A: Find cos(sin(-1/4) – tan(4)). Draw each angle.
Let q=3Dsin-1(-1/4)        = ;            &n= bsp;  Let = α=3Dtan-1(4) =
q=3Dsin-1(-1/4)
x=3DÖ15
α=3Dtan-1(4)<= /div>
Ó F= = r= a= = n= k<= span lang=3DEN-US style=3D'font-size:56%;color:red;mso-fareast-language:ZH-CN'>=  M= = a = 2= = 0= 0= 6
r
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Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0048_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Example A: Find cos(sin(-1/4) – tan(4)). Draw each angle.
Let q=3Dsin-1(-1/4)        = ;            &n= bsp;  Let = α=3Dtan-1(4) =
x=3DÖ15
r=3DÖ17
q=3Dsin-1(-1/4)
α=3Dtan-1(4)<= /div>
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cos(sin(-1/4) – tan(4)) =3D cos(q – α)
x=3DÖ15
q=3Dsin-1(-1/4)
α=3Dtan-1(4)<= /div>
r=3DÖ17
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------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0059.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
cos(sin(-1/4) – tan(4)) =3D cos(q – α)
=3Dcos(q)cos(α) + sin(q)sin(α)
x=3DÖ15
q=3Dsin-1(-1/4)
α=3Dtan-1(4)<= /div>
r=3DÖ17
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cos(sin(-1/4) – tan(4)) =3D cos(q – α)
=3Dcos(q)cos(α) + sin(q)sin(α) ; use the drawings
=3D
x=3DÖ15
q=3Dsin-1(-1/4)
α=3Dtan-1(4)<= /div>
Ö15
4
Ö17
1
+
(-1)
4
Ö17
4
r=3DÖ17
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cos(sin(-1/4) – tan(4)) =3D cos(q – α)
=3Dcos(q)cos(α) + sin(q)sin(α) ; use the drawings
=3D
=3D        = ;       » -0.00770
x=3DÖ15
q=3Dsin-1(-1/4)
α=3Dtan-1(4)<= /div>
Ö15
4
Ö17
1
+
(-1)
4
Ö17
4
Ö15 – 4
4Ö17
r=3DÖ17
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file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0058_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPAAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA6 ABwAgAAAAAAAAAJVjI+py+0Iopy02oszMLr7X3HgSFpiiZJnynZrC5tBTMv1Lb04rO9s70MBg6oZ kWc8/pJKIbNZhKaG0gy1erliQ8+tRuvNdcPZMZl7dpnT4of7DV8UAAA7 ------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Your turn=
= Find sin(c= os-1(-1/3) – tan-1(-2/5)). Draw each = angle. = ;
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0031.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Example B: Find sin(2tan(-7/4)). Draw the angle.
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0060.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Let α=3Dtan-1(-7/4)
Example B: Find sin(2tan(-7/4)). Draw the angle.
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0061.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Let α=3Dtan-1(-7/4)
Example B: Find sin(2tan(-7/4)). Draw the angle.
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More Examples on Inverse Trigonometric Functions and Formulas
Let α=3Dtan-1(-7/4)
r=3DÖ65
Example B: Find sin(2tan(-7/4)). Draw the angle.
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on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Let α=3Dtan-1(-7/4)
r=3DÖ65
sin(2tan(-7/4))
=3D sin(2α)
Example B: Find sin(2tan(-7/4)). Draw the angle.
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More Examples on Inverse Trigonometric Functions and Formulas
Let α=3Dtan-1(-7/4)
r=3DÖ65
sin(2tan(-7/4))
=3D sin(2α)=3D 2sin(α)cos(α)
Example B: Find sin(2tan(-7/4)). Draw the angle.
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More Examples on Inverse Trigonometric Functions and Formulas
Let α=3Dtan-1(-7/4)
r=3DÖ65
sin(2tan(-7/4))
=3D sin(2α)=3D 2sin(α)cos(α)
=3D 2
Example B: Find sin(2tan(-7/4)). Draw the angle.
Ö65
(-7)
Ö65
4
*
*
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More Examples on Inverse Trigonometric Functions and Formulas
Let α=3Dtan-1(-7/4)
r=3DÖ65
sin(2tan(-7/4))
=3D sin(2α)=3D 2sin(α)cos(α)
=3D 2
=3D
Example B: Find sin(2tan(-7/4)). Draw the angle.
Ö65
(-7)
Ö65
4
*
*
65
-56
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More Examples on Inverse Trigonometric Functions and Formulas
Example C: Find cos(        = ;       ). Draw the angle.
cos-1(-3/4)
2
------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0067_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABE AAEAgAAAAAAAAAIHjI+py+1vCgA7 ------=_NextPart_01C816F0.13C07040 Content-Location: file:///C:/4D764A33/4MoreExamplesonInverseTrigonometricFunctions_files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" More Examples on Inverse Trigonometric Functions and Formulas
More Examples on Inverse Trigonometric Functions and Formulas
Let A=3D