The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) are discussed. These include the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points.

2022年1月21日 · Give an example of the largest interval you can find on which \(f(t) = \sin(t)\) is decreasing and concave down. Give an example of the largest interval you can find on which \(g(t) = \cos(t)\) is increasing.

There are six trigonometric functions sin θ, cos θ, tan θ, cot θ, tan θ, cosec θ, and sec θ. The domain and range of trigonometric functions are given by the angle θ and the resultant value, respectively. the range is the set of all or some real numbers.

Graph the equation in order to determine the intervals over which it is increasing or decreasing. Increasing on: (π 2 +πn,∞) (π 2 + π n, ∞) Decreasing on: (−∞, π 2 +πn) (- ∞, π 2 + π n)

2024年4月12日 · One way to graph the function y = sin(x) is to construct a table of x and y values for y = sin(x). Table 5.5.1 lists some of the values for the sine function. Plotting the points from the table and continuing along the x -axis gives the shape of the sine function, which is illustrated in the figure below.

The graph of y = sin ax. Since the graph of y = sin x has period 2 π, then the constant a in. y = sin ax. indicates the number of periods in an interval of length 2 π. (In y = sin x, a = 1.) For example, if a = 2 --y = sin 2x-- that means there are 2 periods in an interval of length 2 π. If a = 3 --y = sin 3x-- there are 3 periods in that ...

Sine Function: f(x) = sin (x) • Graph • Domain: all real numbers • Range: [-1 , 1] • Period = 2π • x intercepts: x = kπ , where k is an integer. • y intercepts: y = 0 • Maximum points: (π/2 + 2kπ, 1), where k is an integer. • Minimum points: (3π/2 + 2kπ, -1), where k is an integer. •

We then define the cosine and sine of the arc t as the x and y coordinates of the point P, so that P(t) = (cos(t), sin(t)) (we abbreviate the cosine as cos and the sine as sin). So the cosine and sine values are determined by the arc t and the cosine and sine are functions of the arc t.

Intervals with а constant sign: sinx>0 (sine function takes positive values) for all x on the interval (0; π), and on all intervals obtained by shifting the interval (0; π) by 2πn, where n∈Z (i.e. sinx>0 for x∈(2π·n, π+2π·n), n∈Z.

Between $0$ to $2π$, I have noticed that $\sin x$, $\cos x$ and $\tan x$ values repeat for different values of $x$. For example, $\sin 30 = \sin 150$ What exactly is the interval between two successive values of $x$ such that the value of $\sin x$, $\cos x$ or $\tan x$ are equal?