Trig Math Problem

[silveryhair]

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The problem reads: What is the maximum value for the expression
2Sin(pi+x) + sin(x) + 2

Can anyone tell me why 2Sin (pi+x) = -2sin(x)

Thanks!

 

[Streetwolf]

The problem reads: What is the maximum value for the expression
2Sin(pi+x) + sin(x) + 2

Can anyone tell me why 2Sin (pi+x) = -2sin(x)

Thanks!

The points on the circle of sin(x) and sin(pi + x) would be like picturing the endpoints of any diameter you can think of going across the unit circle (for instance sin(0) and sin(pi) would represent endpoints of a horizontal diameter). Now that you can imagine that, just rotate the diameter in any direction and you'll see that the y-value of one endpoint is always the negative value of the y-value of the other endpoint. Thus sin(pi+x) = -sin(x)... then you just multiply both sides by 2 and you get your equation.

Mathematically:

sin(x + y) = sin(x)cos👍 + cos(x)sin👍

sin(pi + x) = sin(pi)cos(x) + cos(pi)sin(x)
= 0 * cos(x) + (-1) * sin(x)
= 0 - sin(x)
= -sin(x)

Thus sin(pi + x) = -sin(x) and so 2sin(pi + x) = -2sin(x).

 

[silveryhair]

Thanks Streetwolf!!!