How to Find the Period of a Trig Function
- Solution The secant and cosecant graphs have the same general shape. ...
- Solution To do this, look at the two functions on the same graph. ...
- Solution First, find a sine equation. ...
- Solution Begin with c o t ( 9 x). ...
- Solution This cosecant function will have the form a c s c ( b x + c) + d. ...
What is the trigonometric function's period?
Period of a Trigonometric Function The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period. For any trigonometry graph function, we can take x = 0 as the starting point.
How to multiply through a trig equation with another function?
- Use the sine double-angle identity to create a substitution for the expression on the left. ...
- Replace the expression on the left of the original equation with its equivalent from the double-angle identity.
- Multiply each side of the equation by 2.
- Rewrite the expression as an inverse function. ...
How to find the period of the tangent?
x -intercept : n π , where n is an integer. The tangent function does not have an amplitude because it has no maximum or minimum value. The period of a tangent function, y = a tan ( b x) , is the distance between any two consecutive vertical asymptotes. Also see Trigonometric Functions .
How to find the vertical shift of a trig function?
How To Find Vertical Shift? Step 1: Remember the general form of a trig function. If you divide the C by the B (C / B), you’ll get your phase shift. The D is your vertical shift. The vertical shift of a trig function is the amount by which a trig function is transposed along the y-axis, or, in simpler terms, the amount it is shifted up or down.
What is the formula for f (x + p)?
f (x + p) = f (x) for all x in the domain of f.
How many zeros are there in a half cycle?
There are two zeros that delimit half a cycle. We first find these zeros.
About This Quiz & Worksheet
The worksheet and quiz are available to help you gauge your comprehension of finding the period of a trig function. Different trig functions are addressed on the quiz.
Additional Learning
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What is frequency in trigonometrics?
Frequency is a measure of how often something repeats. Trigonometric functions are repetitive. The trigonometric functions we'll look at today include sine, cosine, tangent, cotangent, secant, and cosecant. We'll plot the function and then measure the period, which is the distance between two identical and consecutive portions of a curve.
How to find frequency of tangent function?
Next, we'll look at the tangent function. The tangent is the sine divided by the cosine. This function is also repetitive so we can find its frequency. The equation which is plotted is y = tan (π t /2).
What is the cosecant function?
Next is the cosecant function. The cosecant function is the reciprocal of the sine function. Plotted is y =csc (π t ).
How to find secant frequency?
And, finally, let's find the frequency of the secant function. The secant is 1/cosine. The function plotted is y = sec (π t ).
What is the frequency of a curve?
This is an easy feature to identify. The period, T = 4 - 2 = 2 seconds. Thus, the frequency, f = 1/ T = 1/2 hertz.
How many seconds is T?
We will assume the units of the horizontal axis are seconds. Thus, T = 2 seconds.
Can we use the same method to determine the frequency of other trig functions?
We can use the same method to determine the frequency of other trig functions. Let's work through a few examples.
How to find period of a number?
This means that to obtain the period, we simply have to divide 2π by |B|, where, |B| is the absolute value of B. To find the absolute value, we just have to take the positive version of the number. For example, if we have -2, its absolute value is 2.
How to modify the period of a cosine function?
The period of the cosine function in its basic form, , is 2π. This period can be modified by multiplying the variable x by a constant.
Is a cosine function a periodic function?
The cosine function is a trigonometric function that is periodic. A periodic function is a function that repeats itself over and over in both directions. The period of the cosine function is 2π, therefore, the value of the function is equivalent every 2π units. For example, we know that we have cos (π) = 1. Every time we add 2π to the x values of the function, we have cos (π+2π). This is equivalent to cos (3π). We have the result cos (π)=1 and since the function is periodic, we also have the result cos (3π) = 1.