how do you find a full cycle of a trigonemtric function?
To find a full cycle of a trigonometric function, you need to consider the period of the function. The period of a trigonometric function is the distance between two consecutive points on the graph where the function repeats itself.
The most commonly used trigonometric functions are sine (sin) and cosine (cos). The period of the sine and cosine functions is 2π radians (or 360 degrees). This means that the function repeats its values every 2π radians or 360 degrees.
So, to find a full cycle of the sine or cosine function, you need to solve for values of the angle θ (measured in radians or degrees) that span an interval of 2π radians or 360 degrees.
For example, to find a full cycle of the sine function, you can start by plotting the graph of the function and then observe where it starts and ends. The sine function reaches its maximum value at π/2 radians (or 90 degrees), then goes to zero at π radians (or 180 degrees), reaches its minimum value at 3π/2 radians (or 270 degrees), and returns back to zero at 2π radians (or 360 degrees).
So, in this case, a full cycle of the sine function is from 0 to 2π radians (or 0 to 360 degrees).
Similarly, you can find a full cycle of the cosine function by observing its graph and identifying points where it starts and ends. The cosine function reaches its maximum value at 0 radians (or 0 degrees), goes to its minimum value at π radians (or 180 degrees), returns back to its maximum value at 2π radians (or 360 degrees), and so on.
Therefore, a full cycle of the cosine function is from 0 to 2π radians (or 0 to 360 degrees).
In summary, to find a full cycle of a trigonometric function, you need to determine the period of the function, which is the distance between two consecutive points where the function repeats itself. For the sine and cosine functions, the period is 2π radians or 360 degrees.