how do u state the period of a function?
for ex.
f(x)=sin((1/2)x)
for y = sin kx, the period is 2pi/k radians or 360/k º
so your period is 360/1/2) = 720º
BTW, the same rule applies to the cosine function, but for the tangent function the period is pi/k radians or 180/kº
To determine the period of a function, you need to observe the behavior of the function within one complete cycle of its graph. In the case of a trigonometric function like f(x) = sin((1/2)x), you can find the period by identifying the value that causes the function to repeat itself.
For the function f(x) = sin((1/2)x), the general form of a sine function is f(x) = a*sin(bx), where 'a' represents the amplitude and 'b' determines the period. In this case, 'a' is equal to 1, and 'b' is equal to 1/2.
The period, denoted by 'P', can be calculated using the formula:
P = (2π) / |b|
Substituting the value of 'b' into the formula, we get:
P = (2π) / |(1/2)|
Now simplify the expression:
P = (2π) / (1/2)
To divide by a fraction, flip the fraction and multiply:
P = (2π) * (2/1)
P = 4π
Hence, for the function f(x) = sin((1/2)x), the period is 4π. This means that the graph of the function repeats itself every 4π units.
Remember, for a general sine function f(x) = a*sin(bx), the period can be found using the formula P = (2π) / |b|.