Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Trig problems

Announcements Posted on
Applying to Uni? Let Universities come to you. Click here to get your perfect place 20-10-2014
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    This is about addition formulae


    Solve the following for 0 <= x <= 2pi

    sin x = 3 cos (x - pi/6)

    ---

    This is what I did (Wrong!)


    sin x = 3 (cos x cos pi/6 + sin x sin pi/6)

    sin x = 3 cos x cos pi/6 + 3 sin x sin pi/6

    sin x - 3 sin x sin pi/6 = 3 cos x cos pi/6

    sin x (1 - 3 sin pi/6) = 3 cos x cos pi/6

    1 - 3 sin pi/6 = 3 cot x cos pi/6

    and now I'm stuck...

    help..

    Jorge
    • 55 followers
    Offline

    ReputationRep:
    Well, sin(pi/6) = 0.5, and cos(pi/6) = (rt3)/2

    So, that should help. From then on, it's just a matter of rearranging for cotx, and then solving.
    • 3 followers
    Offline

    ReputationRep:
    sinx = 3cos(x-pi/6)

    cos(x-pi/6) = cos(x)cos(pi/6) - sin(x)sin(pi/6)
    cos(x-pi/6) = cos(x)sqrt3/2 - sin(x)/2

    sinx = 3[cos(x)sqrt3/2 - sin(x)/2]
    sinx = {(3sqrt3)/2}cosx - (3/2)sinx
    5/2sinx = {(3sqrt3)/2}cosx
    tanx = {(3sqrt3)/2}/(5/2)
    tanx = {(3sqrt3)/2}.(2/5)
    tanx = {(6sqrt3)/10}
    tanx = {(3sqrt3)/5

    x = 0.805
    x = 3.95
    • 0 followers
    Offline

    ReputationRep:
    (Original post by El Stevo)
    sinx = 3cos(x-pi/6)

    cos(x-pi/6) = cos(x)cos(pi/6) - sin(x)sin(pi/6)
    cos(x-pi/6) = cos(x)sqrt3/2 - sin(x)/2

    sinx = 3[cos(x)sqrt3/2 - sin(x)/2]
    sinx = {(3sqrt3)/2}cosx - (3/2)sinx
    5/2sinx = {(3sqrt3)/2}cosx
    tanx = {(3sqrt3)/2}/(5/2)
    tanx = {(3sqrt3)/2}.(2/5)
    tanx = {(6sqrt3)/10}
    tanx = {(3sqrt3)/5

    x = 0.805
    x = 3.95
    cosx cos(pi/6)+sinxsin(pi/6)
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    (Original post by El Stevo)
    sinx = 3cos(x-pi/6)

    cos(x-pi/6) = cos(x)cos(pi/6) - sin(x)sin(pi/6)
    cos(x-pi/6) = cos(x)sqrt3/2 - sin(x)/2

    sinx = 3[cos(x)sqrt3/2 - sin(x)/2]
    sinx = {(3sqrt3)/2}cosx - (3/2)sinx
    5/2sinx = {(3sqrt3)/2}cosx
    tanx = {(3sqrt3)/2}/(5/2)
    tanx = {(3sqrt3)/2}.(2/5)
    tanx = {(6sqrt3)/10}
    tanx = {(3sqrt3)/5

    x = 0.805
    x = 3.95
    Thanks everybody, I got it

    sinx = 3(cosx sqrt3/2 + sinx/2)

    -sinx/2 = cosx 3sqrt3/2

    sinx = - cos 3sqrt3

    tanx = - 3sqrt3 = -1.38

    between 0 and 2pi > 1.76 and 4.90

    Thanks
    • 0 followers
    Offline

    ReputationRep:
    (Original post by Jorge)
    Thanks everybody, I got it

    sinx = 3(cosx sqrt3/2 + sinx/2)

    -sinx/2 = cosx 3sqrt3/2

    sinx = - cos 3sqrt3

    tanx = - 3sqrt3 = -1.38

    between 0 and 2pi > 1.76 and 4.90

    Thanks
    yep same as my answer
Updated: January 15, 2005
New on TSR

A-level results day

Is it about making your parents proud?

Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.