Answer: Hence, the set of zeros of sine function is: x=kπ where k∈ integers.

Use the equation period=2pi/IbI to solve for the absolute value of b and plug it into the equation.

Explanation: The amplitude and period of y = a sin (bx + c ) are a and 2πb . Here, a = 1 and b = 4. This sine wave oscillates between the crests at y = 1 and the lowest points at y=−1 , periodically, with period π2 for one full wave.

The trigonometric functions sine and cosine are common periodic functions, with period 2π (see the figure on the right).

In order to determine periodicity and period of a function, we can follow the algorithm as :

1. Put f(x+T) = f(x).
2. If there exists a positive number “T” satisfying equation in “1” and it is independent of “x”, then f(x) is periodic.
3. The least value of “T” is the period of the periodic function.

A signal is a periodic signal if it completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods. The completion of a full pattern is called a cycle. A period is defined as the amount of time (expressed in seconds) required to complete one full cycle.

A function is periodic if its graph repeats after a given length (called the period), sort of like a wave.

Hatching, molting, foraging for food, courtship, and nest building are all examples of common behaviors that may recur at regular intervals. When these periods of activity are repeated at about the same time each day, an animal is said to exhibit diel periodicity (a daily activity cycle).

Sine, cosine, secant, and cosecant have period 2π while tangent and cotangent have period π. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions.

There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as sin, cos, tan, csc, sec, cot. These are referred to as ratios since they can be expressed in terms of the sides of a right-angled triangle for a specific angle θ.

There are three basic trigonometric ratios: sine , cosine , and tangent . Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non- 90° angles.

Trigonometry is used by engineers, medical services technicians, mathematicians, data entry specialists, loggers, statisticians, actuaries, drafters, chemists, economists, physicists, registered nurses, building inspectors, boilermakers, machinists and millwrights.