Help!! Trig question???? (1 Viewer)

[hpahlow]

this question is one that will probably be in my in school exam. can somebody help me out with this please.:rofl:



Show that x=pi/3 is a solution of sin x=1/2 tan x


Then you have to draw them (drawing a tan graph seems impossible in my eyes)

Then it asks you to find all the soultions for the above equation between the x values of pi/2<x<pi/2



if someone could be a legend and help me out with this i would be greatly appreciative

 

[tennille]

For the first part, you can write the question as:
six=sinx/2cosx

The sinxs can cancel out, so you're left with 1/2cosx=1

When you rearrange this, you get cosx=1/2

Then x=pi/3 (or 60 degrees)

 

[webby234]

Well part one is simply

sin(pi/3) = rt3/2

tan(pi/3)/2 = rt3/2

therefore x = pi/3 is a solution.

Here is a tan graph

source: www.mathsrevision.net/gcse/sincostan.gif

For 1/2 tanx just half every y value.

sin x=1/2 tan x
2sin x -sinx/cosx = 0
2sinxcosx - sinx = 0
sinx (2cosx - 1) = 0
so sinx = 0 or cosx = 1/2
x = 0, pi, pi/3, 5pi/3

 

[hpahlow]

thank for that, you guys are the best. i should be ok now :wave: