The cosine of 2pi is 1. In fact, for every integer N, the cosine of 2 N pi is 1.
No
You could just pull out the half: it will be (1/2) cos squared x.
If the sides are 10 cm by x cm by x-2 cm opposite to angle 60 degrees then by substituting the given values into the cosine rule a^2 = b^2 +c^2 -(2bc*cosine A) the value of x works out as 16
The argument of the cosine function must be (2pi/3)*x radians
It could. This is what would happen if it did.
No
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)■
Sine and cosine are cofunctions, which means that their angles are complementary. Consequently, sin (90° - x) = cos x. Secant is the reciprocal of cosine so that sec x = 1/(cos x). Knowing these properties of trigonometric functions, among others, will really help you in other advance math courses.
You could just pull out the half: it will be (1/2) cos squared x.
cos(x) = sin(pi/2-x) = -sin(x-pi/2)
(1 - cos(2x))/2, where x is the variable. And/Or, 1 - cos(x)^2, where x is the variable.
The derivative of cosine of x is simply the negative sine of x. In mathematical terms f'(x) = d/dx[cos(x)] = -sin(x)
No, actually x is the variable in mathematics. cos(x) or cosine is considered a trigonometric function with a variable x.
sin(x) = cos(pi/2 - x). Thus sine is simply a horizontal translation of the cosine function. NB: angles are measured in radians.
Sin(x) cos(x) = 1/2 of sin(2x)
If the sides are 10 cm by x cm by x-2 cm opposite to angle 60 degrees then by substituting the given values into the cosine rule a^2 = b^2 +c^2 -(2bc*cosine A) the value of x works out as 16
half range cosine series or sine series is noting but it consderingonly cosine or sine terms in the genralexpansion of fourierseriesfor examplehalf range cosine seriesf(x)=a1/2+sigma n=0to1 an cosnxwhere an=2/c *integral under limits f(x)cosnxand sine series is vice versa