half range cosine series or sine series is noting but it consdering
only cosine or sine terms in the genral
expansion of fourier
series
for example
half range cosine series
f(x)=a1/2+sigma n=0to1 an cosnx
where an=2/c *integral under limits f(x)cosnx
and sine series is vice versa
Sine and cosine functions represent the ratios of the lengths of sides of a right triangle relative to the hypotenuse. Since these ratios involve the lengths of the triangle's legs (which are always shorter than or equal to the hypotenuse), the values of sine and cosine cannot exceed 1. Additionally, on the unit circle, the coordinates of any point (x, y) are constrained within the range of -1 to 1, which further reinforces that the maximum and minimum values of sine and cosine are also limited to this range.
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 (0) = 1 Sin(0) = 0 The sine and cosine curves are two intertwining curves, that complement each other, hence the words 'Sine (Curve) and Cosine ( COmplementary Curve).
Cotangent is 1 / tangent. Since tangent is sine / cosine, cotangent is cosine / sine.
in trigonometry
Sine(A+ B) = Sine(A)*Cosine(B) + Cosine(A)*Sine(B).
Sine= Opposite/ Hypotenuse Cosine= Adjacent/ Hypotenuse
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
because sine & cosine functions are periodic.
Sine = -0.5 Cosine = -0.866 Tangent = 0.577
No, they do not.
Sine and cosine functions represent the ratios of the lengths of sides of a right triangle relative to the hypotenuse. Since these ratios involve the lengths of the triangle's legs (which are always shorter than or equal to the hypotenuse), the values of sine and cosine cannot exceed 1. Additionally, on the unit circle, the coordinates of any point (x, y) are constrained within the range of -1 to 1, which further reinforces that the maximum and minimum values of sine and cosine are also limited to this range.
The maximum of the sine and cosine functions is +1, and the minimum is -1.
For a right angle triangle:- hypotenuse = adjacent/cosine or hypotenuse = opposite/sine
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.
The derivative of negative cosine is positive sine.