Sin (theta + 180) is equal to -sin (theta) because the sin function is symmetrically opposite every 180 degrees.
Proof:
Draw a unit circle, radius 1, centered at the origin (x=0, y=0). Pick any point on that circle, and draw a line from that point through the origin and to the opposite edge of the circle.
The angle between that line and the x-axis going to the right is theta. It ranges from 0 degrees at (x=1, y=0) to 360 degrees coming back to (x=1, y=0) rotating counter-clockwise. (The angle is called theta to avoid confusion with the question's original use of x.)
The x and y coordinates of the first point are symmetrically opposite the x and y coordinates of the second point. (If X1 were 0.35, for instance, then X2 would be -0.35.) The same goes for Y. (There are two right triangles, with the hypotenuses equal and two angles equal; therefore the two triangles are the same, just flipped over.)
Sin (theta) in a unit circle is defined in trigonometry as y, so sin (theta + 180) is equal to -y, which is the same as -sin (theta).
Sin (theta) is actually y divided by hypotenuse or "opposite over hypotenuse" but, since the hypotenuse is 1, that can be ignored - it does not change the answer.
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x = 116. x + 64 = 180 is the same as x = 180 - 64, which equals 116.
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If x = sin θ and y = cos θ then: sin² θ + cos² θ = 1 → x² + y² = 1 → x² = 1 - y²
Sin[x] = Cos[x] + (1/3)
No. Tan(x)=Sin(x)/Cos(x) Sin(x)Tan(x)=Sin2(x)/Cos(x) Cos(x)Tan(x)=Sin(x)