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    ok - i've now decided that I'm not having a "good trigonometry day" today!

    Express (12 cos θ - 5 sin θ) in the form R cos (θ+α) where R > 0 and 0<α<90°


    thank you for any replies..... (lets hope they don't run away this time - Re:dvs)

    Laura xxxx
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    (Original post by Laura_M)
    ok - i've now decided that I'm not having a "good trigonometry day" today!

    Express (12 cos θ - 5 sin θ) in the form R cos (θ+α) where R > 0 and 0<α<90°


    thank you for any replies..... (lets hope they don't run away this time - Re:dvs)

    Laura xxxx

    R = √(12²+5²) = 13

    13cosα = 12
    cosα = 12/13
    α = 22.6°

    (12 cos θ - 5 sin θ ) = 13cos(θ + 22.6)
    • Thread Starter
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    thanks a lot !

    How do I rep someone? (e.g. you!)
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    click on the weighing scales in the top right corner of my post.
    (feels good to be appreciated)
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    hmmm.... why does 13 cos α = 12 ???
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    acosθ +bsinθ

    R = √(a²+b²)

    R cosα = a
    R sinα = b


    some books use:
    tanα = b/a

    its just the rule
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    If you want a proper explanation:

    12 cos θ - 5 sin θ = R cos ( θ+α )
    _ _ _ _ _ _ _ _ _ = R cosθcosα - R sinθsinα (by compound angle formula)

    Therefore, equating the different terms: 12 cos θ = R cosθcosα , so R cosα = 12
    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _5 sin θ = R sinθsinα , so R sinα = 5

    Treat the statements in bold as simultaneous equations. If you square both of them and add them, you get
    R^2 sin^2 α + R^2 cos^2 α = 12^2 + 5^2
    R^2 ( sin^2 α + cos^2 α ) = 144 + 25
    And since sine squared plus cos squared equals one....
    R^2 = 169
    R = 13

    To get alpha, do "R sinα = 5" / "R cosα = 12"
    i.e.:
    R sinα ` ` 5
    ------ = --
    R cosα ` 12

    R tanα = 5/12

    α = tan^-1 (5/12)
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    yeah... whatever he says
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    (Original post by Undry1)
    yeah... whatever he says
    I use the exact method that "he" uses. It is the proper way.

    [ well they are identical, except the second requires no remembering of rules ]
    • Thread Starter
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    now I'm seriously thinking about giving up...... lol

    Solve, 8 cot θ - 3 tan θ = 2

    0<θ<90°

    answer to 1 dp

    all your replies are greatly appreciated - sometimes it helps to see different explanations - it makes me understand it better

    Laura xxxx


    editted: ok sorry, I've done it now. I should try for longer before I give up!!
 
 
 
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