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Math Help - Need help on some Trig

  1. #1
    Junior Member
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    Need help on some Trig

    Having trouble with these problems can anyone help with any of these questions? And if possible can you explain> been working on this assignment all day and these are the only ones left.

    Find the reference angle for the given angle.
    1. 220
    2. -225
    3. 415

    Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value.

    1. cos(80)cos(10)-sin(80)sin(10)
    2. cos (7pie/6) cos (-pie/ 2)-sin(7pie/6)sine(-pie/2)
    3. sin (255)
    5. cot (135)
    6. sin (5pie/6)

    Find the exact value
    tan(-195)
    tan( -5pie/12)
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  2. #2
    Member billa's Avatar
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    A reference angle is the acute angle (<90) formed with the x-axis and the larger angle.
    For example, a 220 degree angle can be represented by drawing a ray on the positive x-axis and a ray in the third quadrant. The ray in the third quadrant makes an acute angle of 40 with the x-axis. If you draw this out you should understand it pretty easily. The reference angle is always less than 90 degrees and it is between the x-axis and the second ray(the one not on the x-axis) in the larger angle.

    Here are some of the formulas you need - your book should list the subtraction ones (or just let v be negative) - or search on wikipedia
    sin(u+v) = cos(u)sin(v) + sin(u)cos(v)
    cos(u+v) = cos(u)cos(v) - sin(u)sin(v)

    Here is an example:
    cos(u)cos(v)-sin(u)sin(v)=cos(u+v)
    let u=80, let v=10
    cos(u)cos(v)-sin(u)sin(v)=cos(80)cos(10)-sin(80)sin(10)=cos(80+10)=cos(90)=0
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  3. #3
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    Thanks, but I'm still having trouble on

    Use an addition or subtraction formula to find the exact value of the expression.
    and



    would I do it like


    for sin (255) cos(135)sin(120) + sin(120)cos(135) then ? or ?
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  4. #4
    Member billa's Avatar
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    You wrote down the formula wrong, but I think you had the right idea

    sin(255)=cos(135)sin(120) + sin(135)cos(120)


    using the unit circle, sin(120) is the same as sin(60) which is 1/2
    and sin(135) is the same as sin(45) which is (2^(1/2))/2
    cos(135) is equal to -cos(45) so -(2^(1/2))/2
    and cos(120) is -cos(60) so -(3^.5)/2

    Again all of these values can either be read directly off of the unit circle. Depending of how the question is worded you probably could just say sin(120)=.5 etc.

    After you sub. in the values just simplify it and you are done
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