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Math Help - Some more Trig questions

  1. #1
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    Nov 2008
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    Some more Trig questions

    Need some help on these problems. Help would be much appreciated:

    1) find sin x/2, cos x/2, and tan x/2 from the given information:

    cot x = 5, 180 degrees < x < 270 degrees

    2) write the product as a sum

    11 sin x/2 cos x/4

    3) Find sin 2x, cos 2x and tan 2x from the given information

    sec x = 2, x in quadrant IV

    Thanks in Advance
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  2. #2
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    Joined
    May 2008
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    Alright, let me help you:
    1) cot(x)=\frac{1}{tan(x)}=5 <=>1=5*tan(x) <=>\frac{1}{5}=tan(x) <=>arctan(\frac{1}{5})=x

    Take out your calculator, and you will find x=1118'35.8"
    Now 180 < x < 270 , thus the III quadrant, so we add 180 to 1118'35.8" : giving us 191 18' 35.8"

    I guess you can calculate the rest yourself.

    2) This is typical Simpson Formula problem: thus i refer to List of trigonometric identities - Wikipedia, the free encyclopedia

    3)This is more or less tricky. You'd best transform sec(x) into an cos(x)-function:

    \frac{1}{cos(x)}=sec(x)

    since x belongs to the IV quadrant, the cos(x) is equal to cos(x) for x belonging to the I quadrant. Now we do the same as in 1):

    \frac{1}{cos(x)}=2 <=>\frac{1}{2}=cos(x) <=> 45=x

    You can calculate the rest now i guess: sin(2*45)=sin(90)=1 and etcetera

    I hope this solves your problem. One advice for trigonometric problems: learn your table of common sin, cos and tan values at common angles, such as: 30, 60, 90. Have trigonometric fun!
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