Math CentralQuandaries & Queries


Question from Sam, a student:

Find all values of 2sin4x + (Sqrt)3 = 0, in [0, 2pi].

Hi Sam,

There are different ways to approach trig problems, I often think in terms of their graphs. I see the graph of y = sin(t) for t in [0, 2π], t in radians.

y = sin(t)

You have sin(t) = -√3/2 which is approximately -0.8399 so I get two values for t, t1 and t2.

y = sin(t)

I also know from the 1-2-√3 triangle that sin(π/3) = √3/2 and hence the distance labeled a in the diagram is π/3.

y = sin(t)

Hence t1 = π + π/3 = 4π/3 and t2 = 2π - π/3 = 5π/3. Since the sine is periodic with period 2π the solution to sin(t) = -√3/2 is t1 plus or minus multiples of 2π and t2 plus or minus multiples of 2π.

In your problem t = 4x so what solutions do you get for sin(4x) = -√3/2? Which ones are in [0, 2π]?


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS