is sine always less than x?
434022
sin(x) will always range between -1 and 1. It is divergent. It will never converge to a single limiting value as x goes to infinity. c will always be less than x.
295849
with text by Lewis Lehe. Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .
1231934
By convention in Trigonometry, (sinx)2 is written as sin2 x, so # 3 is the correct answer.
978109
The cosecant is the reciprocal of the sine. ... Wherever the sine is positive but less than 1, the cosecant will be positive but greater than 1; wherever the sine is negative but greater than –1, the cosecant will be negative but less than –1.
594641
Intuition states that 1/sin(x) is the same thing as sin -1 (x), just like 2 -1 is the same thing as 1/2. In case you're not familiar with arcsin, it's sort of the reverse operator of sine. You put a ratio of 2 lengths in, and you get an angle out. Same thing for arccos and arctan.
551983
At approx t=-0.26 the sin curve is at zero and rising so theta must be 90 degrees. Whereas the cos curve is at a peak so theta must be 0 degrees. So the cosine wave is 90 degrees out of phase behind the sine wave or 270 degrees out of phase in front of the sine wave.
541898
This is a bit surprising given our initial definitions. and the hyperbolic sine is the function sinhx=ex−e−x2. Notice that cosh is even (that is, cosh(−x)=cosh(x)) while sinh is odd (sinh(−x)=−sinh(x)), and coshx+sinhx=ex.
338930
It answers the question "what angle has sine equal to opposite/hypotenuse?" The symbol for inverse sine is sin-1, or sometimes arcsin.
1240590
The formulae for Sin X is based on the (height)÷(hypotenuse) of a right angled triangle in trigonometry. Therefore X is the angle between the base of a right-angled triangle and the hypotenuse.
1143100
Sine is an odd function, and cosine is an even function. ... A function f is said to be an even function if for any number x, f(–x) = f(x). Most functions are neither odd nor even functions, but some of the most important functions are one or the other.
1157387
Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse . No matter the size of the triangle, the values of sin(θ) and cos(θ) are the same for a given θ, as illustrated below.
659219
The equation sin x = cos x can also be solved by dividing through by cos x. If we put k = 0 and k = 1 we get the solutions /4 (45°) and /4 + = 5 /4 (45°+ 180°= 225°). To solve the inequality sin x > cos x we need to see which is the greater sin x or cos x on the intervals between the solutions /4 and 5 /4.
61011
In particular, the wave Asin(x) has amplitude A because its extreme points are at ±A and its equilibrium would like at 0. The "range" (or "peak-to-peak amplitude") sometimes refers to the difference of largest and smallest values in a wave - so 2A for sin(x).
1325150
Even functions are symmetrical about the y-axis. Odd functions have symmetry about the origin. thus xsinx is an even function. This is graph of xsinx.
39197
The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function. It is simply the vertical distance from the x-axis (or midline) to the highest (or lowest) point on the curve.
50396
Using the unit circle, the sine of an angle t equals the y-value of the endpoint on the unit circle of an arc of length t whereas the cosine of an angle t equals the x-value of the endpoint. See Example. Reference angles can also be used to find the coordinates of a point on a circle. See Example.
596513
In your case, the function cot(x) is defined as 1tan(x) , which is cos(x)sin(x) . So, the zeros of the denominator are the ones of the sine function which, periodicity apart, are 0 and π . So, your vertical asymptotes are vertical lines of equations x=0 and x=π .