MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C8244A.2B5F12D0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C8244A.2B5F12D0 Content-Location: file:///C:/213799D4/sample-4.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Math 240 Test 5 Su/97

Math 240  Sample 4

 

1. Verifying the following identities.

a.  sin(x + y) + sin(x R= 11; y) =3D2sin(x)cos(= y)

b.  tan(x)sin(2x= ) =3D 1– cos(2x)=

 

2.  a. Expand and simplify cos(x – 300o ).

     b. Expand and si= mplify sin(135o + x ).

 

3. a. Given that x is in the 2nd quadrant, y is in the 4th quadrant, sec(x) =3D -3 and tan(y) =3D= -4/3, draw         the angles,  and find s= in(x – y)        =             &nb= sp;     

    b. Given that x is in = the 3rd quadrant, y is in the 4th quadrant, cos(x) =3D -1/3 and tan(y) = =3D -4/3.     =

        Draw the angles and find cos(= x + y)        =             &nb= sp;     

π <&n= bsp; x <  3π/2  and cot(x) =3D 4.

    d. Find cos(x/2) if -<= /span>π= <  x < -<= span style=3D'font-family:"Times New Roman";letter-spacing:-.15pt'>π/2 and csc(x) =3D -4.

    

4. a. Find cos(-π= /12), leave the answer in the exact fo= rm.

    b. Find sin(105o<= /sup>), leave the answer in the exact form.

 

5. = Find the values of the six trigonometric functions of A if cos(2A) =3D -2/5 and = A is in the second quadrant. Draw A.

        =            

6. For each equation, solve for θ where 0 ≤ θ < 2π.  Draw = 52; in the standard position. List all possible θ.

    a.   2sin2(θ) + sin(θ) =3D 0        =             &nb= sp;         b.  cos2( = 52;) =3D 3sin2(θ)

    c.   2tan2(x) =3D tan(x) +1        =             &nb= sp;          d.   cos(2x) + cos(x) =3D 0        =             &nb= sp;       

 

7.&nbs= p; a.  Find all _= 2; where 0 ≤ θ < π and tan(3θ) =3D -1.

     b.  Find all θ where 0 ≤ θ < π and 2sin2(2θ)= =3D 1.

 

8. a.  = Find arctan(tan(-)).

    b.  Find arccos(sin(-)).

 

9.  Dra= w the angles and simplify:

a. cos(arcsin(- 4/7))        =                  =            b. cos(arcsin(-1/3)+arctan(-2))

c. sin(2arcsin(- 2/5))        =             &nb= sp;            =   d. cos(2arctan(-4))

 

10. a. Draw the angle arcsin(1 – u) then simpl= ify tan(arcsin(1 – u ))

      b. Draw the angle arctan(3/u) then simplify sin(arctan(3/u))

 

11. a. Convert (-3, -7) into polar coordinate.  Gi= ve two different versions of the answers.

      b. convert= (4, -23o)p into rectangular form

 

13.  Sk= etch the graph of

      a. r =3D 3= cosq        =             &nb= sp;            =             &nb= sp;          b. π/3 =3D = q       

------=_NextPart_01C8244A.2B5F12D0 Content-Location: file:///C:/213799D4/sample-4_files/image001.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC01Ru0oDURA9c66vrAEXHyAWsqSwUzD+gD8QC5PKxkRYUHA3gQRku3yARUrxSyws rKy0FFs/wVrBde7cG3Fg2DOzZ86ce+/76/M9LPr8cNLwaHYuUOBeFDts2d9FzQY9WtCkiHWEdV1b 50C2rXNIiexVzueaqtznuqK9pTXsoPZDSLV+UvSgmSn3zulM5DTRGUwue9UoV473gi+GCR8t27gv QX2T4LGhDUW79H6/Of0J3JmYZyLtXRX5ODvJb7LTYTEogWlQEazot53cujd48lGsSzmzum17/ytq Vzch7VbFxfAaDDo0V59/eqX4WwJGSOKpEju5GYqaKZaterS7ErLVrcaTvADm3oIm9R18/AJVuRtQ rgEAAA== ------=_NextPart_01C8244A.2B5F12D0 Content-Location: file:///C:/213799D4/sample-4_files/image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQApAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAAU ACIAhAAAAAAAAAUAAA0LCwUIDQgFBQsLDQsIBQ0ICAgIDQgFAAAFCwsFAAsFBQUFCA0ICwsIDQUF CwUABQ0IBQUICwAABQAFCAECAwECAwECAwECAwECAwECAwECAwECAwECAwWRIAAMQhAQYqquQ2EA x7nOIpKIg7LQfMrsOIVpGACmcqhRIdEwtG4zhOMFeEAGEYCUumpAU4cbI7k6kHHTgYSbmlBqUDNg YmwTK6+J5cWgYMFERVoScQF4PYiJiouMjY6PK4GSkwGQlpeYmTwkJmeIai8Hh4oPVGpfjAhZjluO MYZsizFvjjm0jmOPrYoTQ3s8IQA7 ------=_NextPart_01C8244A.2B5F12D0 Content-Location: file:///C:/213799D4/sample-4_files/header.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"

 

 

 

------=_NextPart_01C8244A.2B5F12D0 Content-Location: file:///C:/213799D4/sample-4_files/oledata.mso Content-Transfer-Encoding: base64 Content-Type: application/x-mso 0M8R4KGxGuEAAAAAAAAAAAAAAAAAAAAAPgADAP7/CQAGAAAAAAAAAAAAAAABAAAAAQAAAAAAAAAA EAAAAgAAAAEAAAD+////AAAAAAAAAAD///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////9 /////v////7///8EAAAA/v////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////1IA bwBvAHQAIABFAG4AdAByAHkAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAWAAUA//////////8BAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADC2Uh0HJMgB AwAAAAAEAAAAAAAAXwAxADIANQA2ADIAOAAwADYAMAAwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAABgAAgH/////AgAAAP////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAzwEAAAAAAABfADEAMgA1ADYAMgA4ADAANgAwADEAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGAACAP///////////////wAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgAAADTAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA//////// ////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAA AAIAAAADAAAABAAAAAUAAAAGAAAABwAAAP7///8JAAAACgAAAAsAAAAMAAAADQAAAA4AAAAPAAAA /v////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////8ADAAA eJy7cF7wwcKNUg8Z0IAdAzPDv/+cDGxIYoxQDAYCDAxMUP6/////w4T/j4IhBf4CMQs0DmF4FIwc EMSQD4QlDAoMrgx5QLqIoRK9KMALxBhY4XkeVB4wnWMCix+ASLshq/2wwl+WXeUEIzOQ3cAIK1P8 GXIYUkmyExlwMTAxIvuHWH0iDDD7nYH+z2UoALojiSGLZPuFgPaDvALKQ8TaD1KfBmUzQ+31BIZ+ GtAlZNjPQKr/maHuBYF/0HhDzv+jZcDIAYyQahwF7JAEZWJBIAuSN3KB+RNUNhRjTcv//jNzQdI+ et4XBxK+mclF+cX5aSUKroWliSWZ+XkKxnoGDDxAKZdguBgDN5AP4+gZM3yx3FRIbA5gJlYhViAN xMAczMTAxcjMB/QOU7MxU0sBiDYhSr8MSD9D8mMFKH9HgyfDgyZPiMsYGZkZYeZ2GDEwtRxgBrGM KXIxKuBhEGACtdGYrp69OkdPWmDydA4GbZ2f6/iBYvJgFXIMyHFZwJAIjEtEGQ8rfw0ZDBj8gHIl DJkMZSSUx1LA0APFACsD8eUfC9xtwEhnKGQohdqbD3SZAomuUCCj/AO51YYYhUQCUu2nNqDEfgBm Kkd5/wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMAAB4 nLtwXvDBwo1SDxnQgB0DM8O//5wMbEhijFAMBgIMDExQ/r/////DhP+PgiEF/gIxCzQOYXgUjBwQ xJAPhCUMCgyuDHlAuoihEr0owAvEGFjheR5UHjCdYwKLH4BIuyGrnaAfKMuucoKRGchuYISVKf4M OQypJNmJDLgYmBiR/UOsPhEGmP3OQP/nMhQA3ZHEkEWy/UJA+0FeAeUhYu0HqU+Dspmh9noCQz8N 6BIy7Gcg1f/MUPeCwD9ovCHn/9EyYOQARkg1jgJmiJxn+vfv339iMCMw5TBzQdI+et4XBxK+mclF +cX5aSUKroWliSWZ+XkKxnoGDDxAKZdguBgDN5AP4+gZM3yx3FRIOB2f37P+Pyg1E+tWbFgaaA4w BzMxcDEy8wGzJlOzMVNLAYg2AVkBV7d39Zz//94+BuM/rx/8b82P+v/g1vUAGZB+huTHClA37Wjw ZHjQ5AnJZ4yMzIwwczuMGJhaDjCDWMYw9+9dT7a7ScXI7u+rSP3/9N51r8+f3yjByl9DBgMGP4ZE YA2QyVBGQnksBQw9UHnCykB8+Qcqe+ShbFeGQoZSqL35wDJQgURXKJBR/oHcakOMQiIBqfZTG1Bi PwCA6jmv//////////////////////////////////////////////////////////// ------=_NextPart_01C8244A.2B5F12D0 Content-Location: file:///C:/213799D4/sample-4_files/filelist.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8244A.2B5F12D0--