0
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.
Add your answer:
Earn +20 pts
What is x plus 64 equals 180?
x = 116. x + 64 = 180 is the same as x = 180 - 64, which equals 116.
X plus x plus x equals 180 then what is the value of x?
60
If Sin equals x and Cos equals y then x squared equals what function of y?
If x = sin θ and y = cos θ then: sin² θ + cos² θ = 1 → x² + y² = 1 → x² = 1 - y²
If sin x - cos x equals 1 over 3 what is sin x?
Sin[x] = Cos[x] + (1/3)
Sin x Tan x equals Sin x?
No. Tan(x)=Sin(x)/Cos(x) Sin(x)Tan(x)=Sin2(x)/Cos(x) Cos(x)Tan(x)=Sin(x)
Solve sin 5x plus sin x equals 0?
Assuming the angles are expressed in radians:sin(5x) + sin(x) = 0∴ sin(5x) = -sin(x)∴ 5x = x + π∴ x = π/4On the other hand, if your angles are in degrees, then the answer would be:sin(5x) + sin(x) = 0∴ sin(5x) = -sin(x)∴ 5x = x + 180∴ x = 180°/4∴ x = 45°
What is x plus 64 equals 180?
x = 116. x + 64 = 180 is the same as x = 180 - 64, which equals 116.
Verify cot x-180 cot x?
cot x = (cos x) / (sin x) cos (x - 180) = cos x cos 180 + sin x sin 180 = - cos x sin (x - 180) = sin x cos 180 - cos x sin 180 = - sin x cot (x - 180) = (cos (x - 180)) / (sin (x - 180)) = (- cos x) / (- sin x) = (cos x) / (sin x) = cot x
55 plus what equals 180?
55 + x = 180 x = 180 - 55 x = 125
X plus x plus x equals 180 then what is the value of x?
60
How do you solve Sin x plus sin 3x plus sin 5x plus sin 7x equals?
sin7x-sin6x+sin5x
X-39 plus x plus 61 equals 180?
x= 119
Who formulated eix equals cos x plus you sin x?
leonhard euler
What is x if 10x plus 22 plus 4x plus 70 equals 180?
x = 6 and 2/7
What is x if 9X plus 18 equals 180?
9x+18 = 180 9x = 180-18 9x = 162 x = 18
What is the answer to 90 plus x plus 72 plus 30 equals 180 solve for x?
90+x+72+30 = 180. If you add 90+72+30, you get 192. But to get 180 you have to subtract 12. 90+(-12)+72+30 =180 if x is -12
2 cot x plus 1 equals -1?
2 cot(x) + 1 = -1 2 cot(x) = -2 cot(x) = -1 cos(x)/sin(x) = -1 cos(x) = - sin(x) x = 135°, 315°, 495°, ... another one every 180 degrees
