First of all, I can't tell what angle you're talking about, because you failed
to mention the unit of your angle.
-- Cosine of 16 degrees is roughly 0.9613 ... a positive number.
-- Cosine of 16 radians is roughly -0.9577 ... a negative number.
-- Cosine of 16 grads is roughly 0.9686 ... a positive number.
Over any reasonably large range of angles, half of them have positive cosines,
and the other half of them have negative cosines.
Cosine to the negative first power and cosine cancel each other out because cosine to the negative first power is one over cosine, and one over anything times anything is just one.
Because the cosine of some angles is positive and the cosine of some other angles is negative.
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
cosine(x) = -1x = (270 + 360N) degreesorx = (1.5 + 2N) pi radiansN is any integer, positive or negative.
225 degrees
The derivative of negative cosine is positive sine.
Cosine to the negative first power and cosine cancel each other out because cosine to the negative first power is one over cosine, and one over anything times anything is just one.
Because the cosine of some angles is positive and the cosine of some other angles is negative.
All the angles in 4th quadrant have positive cosine and negative sine e.g. 280,290,300,310...etc.
[ cos(Θ) ]-1 = 1/cosine(Θ) = secant(Θ)
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
The second quadrant (top left).
The anti derivative of negative sine is cosine.
The negative sine graph and the positive sine graph have opposite signs: when one is negative, the other is positive - by exactly the same amount. The sine function is said to be an odd function. The two graphs for cosine are the same. The cosine function is said to be even.
cosine(x) = -1x = (270 + 360N) degreesorx = (1.5 + 2N) pi radiansN is any integer, positive or negative.
225 degrees
It doesn't really. Depending on the exact value of the argument, the cosine function can give both positive and negative results, for a negative argument. As to "why" the sine, or cosine, functions have certain values, just look at the function definition. Take points on a unit circle. The sine represents the y-coordinate for any point on the circle, while the cosine represents the x-coordinate for such a point. (There are also other ways to define the sine and the cosine functions.)