No, it does not.
∫ -cos(x) dx = -sin(x) + C
Negative cosine f(x) = sin(x) f'(x) = -cos(x)
You could just pull out the half: it will be (1/2) cos squared x.
No
Yes. Cosine is adjacent side over hypothenuse. Adjacent side is the same sign when x is positive or negative.
The cosine is simply the x-coordinate of the unitary circle. It helps to draw the circle, and the sine and cosine (x and y coordinates), to visualize this. The y-coordinate is the same for a positive angle and for the corresponding negative angle.
This is going to require some visualization. Cosine is defined as the x-value on the unit circle. If you picture where a point would be, for example, at the angle of pi/6 (30°) you get a coordinate of (√(3)/2 , 1/2) so cosine is √(3)/2 and sine is 1/2 To find a negative angle you take the reflection across the x-axis. Since this does not chance the x-value, only the y, cosine does not change. The coordinates of -(pi/6) (-30°) are (√(3)/2 , -1/2). cos(-x) = cos(x) sin(-x) = - sin(x)■
No, it does not.
∫ -cos(x) dx = -sin(x) + C
Negative cosine f(x) = sin(x) f'(x) = -cos(x)
You could just pull out the half: it will be (1/2) cos squared x.
Sin(x) cos(x) = 1/2 of sin(2x)
y=3cos(x) peroid is 2pie
f(x) = Cos(x) f'(x) = -Sin(x) Conversely f(x) = Sin(x) f'(x) = Cos(x) NB Note the change of signs.
No
x-1 means 1/x, also called the reciprocal of x.