2007-12-05 21:24:55 · 8 answers · asked by Sunshine 2 in Science & Mathematics ➔ Mathematics
if you look at positive x, it is measuring the angle in the counterclockwise direction starting with the positive x-axis. therefore, -x would go in the clockwise direction starting with the positive x-axis. Cosine is positive in two quadrants, I, and IV (All Students Take Calculus). Now if it starts in the 1st quadrant (positive x), cosine is positive. If it starts off in the 4th quadrant (negative x) cosine is still positive. Thus, cos(x) = cos(-x)
2007-12-05 21:32:17 · answer #1 · answered by ProSingerWannaBe 2 · 0⤊ 0⤋
The simple answer is, because cosine is symmetric with respect to the Y-axis. And it is so, because it's a cyclical waveform with a maximum value (minimum also works) when x = 0.
Think of it this way: draw a cosine in both directions. Now, imagine a mirror aligned along the Y-axis.. what you see, a reflection of the X axis and cosine going positive, looks exactly like the negative going X axis and cosine graph.
Any function that's symmetric about the Y-axis will be the same for negative as for positive values of X. In fact, in mathematics, another name for this "mirror symmetry" is "even symmetry"... and "cosine symmetry".
I'm sure there's a reasonable mathematical proof of this, if you're not graphically oriented.. maybe expanding cos(x) and cos(-x) in a Taylor series, that kind of thing.
2007-12-05 21:40:54 · answer #2 · answered by Hazydave 6 · 0⤊ 0⤋
Cos = adjacent/hypotenuse sides of the triangle.
The adjacent sides would be the only side in the triangle to have negative values, since it is the only line to have symmetry in the x-axis.
Another reason would be that
sin(x) = cos (90-x)
2007-12-05 21:38:58 · answer #3 · answered by denarea3 2 · 0⤊ 0⤋
Consider rotating vector r making angle θ with x axis.
r has co- ordinates (x,y)
1st quadrant
cos θ = x / r
4th Quadrant
cos (- θ ) = cos (360 - θ) = x / r
Thus cos θ = cos (- θ)
2007-12-05 21:42:39 · answer #4 · answered by Como 7 · 2⤊ 0⤋
Because of unit circle.They have the same segment on the horizontal axis.
2007-12-05 21:32:24 · answer #5 · answered by Anonymous · 0⤊ 0⤋
They are basic results which are to be accepted as they are.There is no explanation.They have been formed to create new trigo identities of various angles.
2007-12-05 21:35:19 · answer #6 · answered by ksh_great 1 · 0⤊ 0⤋
cos(x) + cos(-x)= 2cos((x+(-x))/2)*cos((x-(-x))/2)
= 2 cos(0) * cosx
= 2cos x ,( cos(0)=1)
=> cos(-x)= cos(x)
2007-12-05 21:57:33 · answer #7 · answered by namvt2000 6 · 0⤊ 1⤋
because maths isnt meant to make sense :D
2007-12-05 21:28:24 · answer #8 · answered by G4V1N 2 · 0⤊ 1⤋