Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.
Hanley Rd, Suite St. Louis, MO Subject optional. Email address: Your name:. Example Question 29 : Trigonometry. Possible Answers:. Correct answer:. Explanation : The standard period of a tangent function is radians. Therefore, you will have a function of the form: Since and do not alter the period, these can be anything. Report an Error. Thus, you will have a function of the form: Since and do not alter the period, these can be anything.
Example Question 31 : Trigonometry. What is the period of the following tangent function? Explanation : The period of the tangent function defined in its standard form has a period of.
Example Question 32 : Trigonometry. Explanation : For tangent and cotangent the period is given by the formula: where comes from. Example Question 33 : Trigonometry. If we don't specify a period and just say "with period k" it is understood that k is the smallest non-zero period. But there's nothing paradoxical that tan may also have a smaller period.
Your observation of "anti-period" explains why. It could be any submultiple or the combination might be constant or zero. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Log in. What does this tell us about the output of these functions? Let's talk about this question were given that the tangent and co tangent of a time period of pie. So what what does this tell us about the output of these functions through the meaning of the time period?
So if we are given that the time period of any function in this question has given us by for court and gender and tangent. So it means that after pie, after an in developed by, it repeats itself. So we can say that output output of these functions repeat after each cycle of uh by. So it means that we can say that F of X plus pi is nothing worth fx. So even after adding the pie, what you get as same as what you got initially.
So in other words, it repeats itself after every pie, every interval of by. So that is what I mean. That is what is the significance of the output with respect to the time period. Thank you. Explain what is meant by the period of a trigonometric function. The horizontal stretch can typically be determined from the period of the graph. With tangent graphs, it is often necessary to determine a vertical stretch using a point on the graph.
Because there are no maximum or minimum values of a tangent function, the term amplitude cannot be interpreted as it is for the sine and cosine functions. To make the function approach the asymptotes at the correct rate, we also need to set the vertical scale by actually evaluating the function for at least one point that the graph will pass through.
For example, we can use. At a quarter period from the origin, we have. This means the curve must pass through the points 0. The only inflection point is at the origin. Figure shows the graph of one period of the function. In this case, we add C and D to the general form of the tangent function. The graph of a transformed tangent function is different from the basic tangent function tan x in several ways:. Step 1. Step 3. Step 4. Step 5—7.
The graph is shown in Figure 4. Step 2. Many real-world scenarios represent periodic functions and may be modeled by trigonometric functions. Have you ever observed the beam formed by the rotating light on a police car and wondered about the movement of the light beam itself across the wall?
The periodic behavior of the distance the light shines as a function of time is obvious, but how do we determine the distance? We can use the tangent function. We see that the stretching factor is 5. This means that the beam of light will have moved 5 ft after half the period.
This means that every 4 seconds, the beam of light sweeps the wall. The distance from the spot across from the police car grows larger as the police car approaches. See Figure 8. Because the cosine is never more than 1 in absolute value, the secant, being the reciprocal, will never be less than 1 in absolute value.
See Figure 9. The graph of the cosine is shown as a dashed orange wave so we can see the relationship. Where the graph of the cosine function decreases, the graph of the secant function increases. Where the graph of the cosine function increases, the graph of the secant function decreases. When the cosine function is zero, the secant is undefined. The secant graph has vertical asymptotes at each value of x where the cosine graph crosses the x -axis; we show these in the graph below with dashed vertical lines, but will not show all the asymptotes explicitly on all later graphs involving the secant and cosecant.
Note that, because cosine is an even function, secant is also an even function.
0コメント