Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    "It is given that 5sin3x = 2cos3x, what is tan3x equal to"

    Im sure its something to do witht he fact that tan x = sinx/cosx but i dont know what to do from there.

    If I let 3x = z then:

    (5/2)tan z = 5sin z / 2cos z

    ... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    tan3x = sin3x/cos3x

    Does that help at all?

    EDIT: If you let 3x=z then:
    5sinz=2cosz

    divide both sides by cosz:
    5sinz/cosz = 2

    Now divide both sides by 5:
    sinz/cosz = 2/5
    Offline

    2
    ReputationRep:
    tan3x = sin3x/cos3x
    Online

    2
    ReputationRep:
    5sin3x = 2cos3x
    5/2 = sin3x/cos3x
    5/2 = tan3x
    x = (tan^-1 (5/2))/3

    tap it into a calculator to see if it works..
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Slick168)
    5sin3x = 2cos3x
    5/2 = sin3x/cos3x
    5/2 = tan3x
    x = (tan^-1 (5/2))/3

    tap it into a calculator to see if it works..
    That's not right.
    Offline

    0
    ReputationRep:
    answer is 2/5
    Offline

    0
    ReputationRep:
    (Original post by dealer91)
    "It is given that 5sin3x = 2cos3x, what is tan3x equal to"

    Im sure its something to do witht he fact that tan x = sinx/cosx but i dont know what to do from there.

    If I let 3x = z then:

    (5/2)tan z = 5sin z / 2cos z

    ... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.
    5sin3x = 2cos3x

    divide through by cos(3x)

    5(sin(3x)/cos(3x))=2

    then divide by 5, and as sin(3x)/cos(3x) = tan(3x) you get

    tan(3x) = 2/5

    is that what u wanted??
    Offline

    0
    ReputationRep:
    (Original post by dealer91)
    ... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.
    You know 5/2 tan z = 5sinz/2cosz.

    Now look at the original equation and try and see what 5sinz/2cosz must be.
    Offline

    13
    ReputationRep:
    (Original post by dealer91)
    "It is given that 5sin3x = 2cos3x, what is tan3x equal to"

    Im sure its something to do witht he fact that tan x = sinx/cosx but i dont know what to do from there.

    If I let 3x = z then:

    (5/2)tan z = 5sin z / 2cos z

    ... but that doesn't help me... i know the answer is something involving the 5 and the 2 but Im not getting there.
    5\mathrm{sin}3x = 2\mathrm{cos}3x

    \frac{5\mathrm{sin}3x}{\mathrm{c  os}3x} = 2

    5\frac{\mathrm{sin}3x}{\mathrm{c  os}3x} = 2

    \frac{\mathrm{sin}3x}{\mathrm{co  s}3x} = \frac{2}{5}

    \mathrm{tan}3x = \frac{2}{5}

    3x = \mathrm{arctan}\frac{2}{5}

    x = \frac{1}{3}\mathrm{arctan}\frac{  2}{5}
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ah yeah I see iot now thanks
    Online

    2
    ReputationRep:
    ... that was BASIC ALGEBRA!!! what are they teaching you kids nowadays. hehe i htink i got confused with tryign to write it out correctly lolx
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 15, 2008

University open days

  • Heriot-Watt University
    School of Textiles and Design Undergraduate
    Fri, 16 Nov '18
  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.