# How to graph a sin function with respect to it's limits and x intercepts

• Trespaser5
In summary, the conversation discusses how to sketch the curve of y=sin(x) and find the x intercepts mathematically. It is explained that periodic functions, such as sin(x), have a period in which the function repeats itself. Therefore, the x intercepts can be found by setting y=0 and solving for x. It is also mentioned that the calculator should be in radian mode when working with trigonometric functions.
Trespaser5
I have been given a question to sketch the curve of y=sin(x). I have looked into finding the domain which I understand but I don't understand how I prove the x intercepts mathematically as when I make x=0 I obviously get a 0 value for y but a sin curve obviously intercepts and pi and 2pi etc, how do I prove this ? Also why when I put sin(3pi/2) into the calculator do I not get a negative figure ? or why when I put pi and 2pi in do I not get zero ?

sorry, i didn't have my calculator in radian mode. Still I don't understand how I get the values of the x intercepts mathamatically in the same way as you do with polynomial expressions ?

It's actually part what periodic functions are.
for a periodic function g(x): g(x+P)=g(x) where P is the period.
So your function $f(x)=sin(x)$ is as good as $f(x)=sin (x \pm n\pi)$ n=0,1,2...
so $x=sin^{-1}(y) \pm n\pi$
now go ahead and put y=0 to get all your x intercepts.

that's the key to the door, thankyou :)

I've been trying all week but what I can't understand is that as [sin][/-1](0) is always 0 then any value I put in between 0 and 2∏ I get that value as an x intercept, where am I getting confused ?

## 1. How do I find the x-intercepts of a sin function?

To find the x-intercepts of a sin function, set the function equal to 0 and solve for x. This will give you the values where the function crosses the x-axis.

## 2. What are the limits of a sin function?

The limits of a sin function depend on the range of values for x. For example, if x is restricted to values between 0 and 2π, the limits of the sin function would be -1 and 1. However, if there are no restrictions on x, the limits would be -∞ and ∞.

## 3. How do I graph a sin function?

To graph a sin function, plot the x and y coordinates for several points using the equation y = sin(x). Then, connect the points with a smooth curve. Don't forget to label the x and y axes and include the appropriate scale.

## 4. What is the period of a sin function?

The period of a sin function is the distance between two consecutive peaks or troughs of the graph. It can be calculated using the equation T = 2π/b, where b is the coefficient of x in the sin function.

## 5. How do I find the amplitude of a sin function?

The amplitude of a sin function is the distance from the center line to the peak or trough of the graph. It can be calculated using the equation A = |b|, where b is the coefficient of x in the sin function.

• Calculus and Beyond Homework Help
Replies
5
Views
217
• Calculus and Beyond Homework Help
Replies
12
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
3K
• Calculus and Beyond Homework Help
Replies
10
Views
756
• Calculus and Beyond Homework Help
Replies
10
Views
975
• Calculus and Beyond Homework Help
Replies
2
Views
409
• Calculus and Beyond Homework Help
Replies
3
Views
756
• Calculus and Beyond Homework Help
Replies
1
Views
8K
• Calculus and Beyond Homework Help
Replies
18
Views
2K
• Precalculus Mathematics Homework Help
Replies
6
Views
1K