Find the value of sinx+sin(x+2pi)+sin(x+4pi)

Question

If sinx= -0.3,

Answer 1

Hi Latika,

 

All trig functions (sin, cos, tan, etc) are periodic functions; they repeat their pattern of values exactly if you add their period to the angle inside.

 

The period for sin and cos is 360° = 2π. If you think about it, this makes sense, because adding a full rotation to your angle puts you back in the same spot on the unit circle.

 

For your problem, what this means is that

sin x = sin(x + 2π)

and

sin x = sin(x + 2π + 2π) = sin(x + 4π)

 

 

Therefore,

sin x + sin(x + 2π) + sin(x + 4π)

 = -0.3 + -0.3 + -0.3

 = -0.9