# Solve for Sin teta=0 | Math Homework Help

• lioric
In summary, the conversation discusses a problem involving the values of sin and cos teta, and the confusion surrounding the equation sin teta = 0. The expert explains that the book's explanation is poorly worded and that there are actually multiple solutions to the problem in the given interval. They also suggest plotting the graphs of the equations to better visualize the solutions. Overall, the expert's explanation is deemed to be helpful and clear.
lioric

## The Attempt at a Solution

The first picture is the question
The second picture is the marking scheme
I have circled in yellow the problem
I would like to know how sin teta = 0
Thank you

lioric said:
I would like to know how sin teta = 0
Thank you

What don't you understand about it?

PeroK said:
What don't you understand about it?
I do know how cos teta = 1/3
But the sin teta part I don't get I couldn't transpose the formula 3sin teta = sin teta / cos teta to sin teta = 0
So I know I m missing something fundamental

lioric said:
I do know how cos teta = 1/3
But the sin teta part I don't get I couldn't transpose the formula 3sin teta = sin teta / cos teta to sin teta = 0
So I know I m missing something fundamental

What is ##\tan(0)##?

What is ##3\sin(0)##?

PeroK said:
What is ##\tan(0)##?

What is ##3\sin(0)##?
Both is 0

lioric said:
Both is 0

So, ##\theta = 0## is a solution to your equation ##\tan \theta = 3\sin \theta##.

What about other values of ##\theta## where ##\sin \theta = 0##?

berkeman
PeroK said:
So, ##\theta = 0## is a solution to your equation ##\tan \theta = 3\sin \theta##.

What about other values of ##\theta## where ##\sin \theta = 0##?

Hmmm I guess I know what your saying
Teta= 180
That part I understand
Thank you very much

lioric said:

## Homework Statement

View attachment 109209
View attachment 109210

## The Attempt at a Solution

The first picture is the question
The second picture is the marking scheme
I have circled in yellow the problem
I would like to know how sin teta = 0
Thank you

The book's explanation is poorly worded; it should have said ##\cos(\theta) = 1/3## OR ##\sin(\theta) = 0##. That means that one or the other of those two possibilities can occur, and that corresponds to the existence of more than one solution to the problem in the interval ##0^o < \theta < 360^o##.

If you plot the graphs of ##y = 3\sin(\theta)## and ##y = \tan(\theta)## over the interval ##0^o < \theta < 360^o##, you will see that there are three points where the two graphs cross (five points of crossing if you include ##\theta = 0^o## and ##\theta =360^o##). The equation ##\sin(\theta) = 0## has one solution in ##(0^0,360^o)##, while the equation ##\cos(\theta) = 1/3## has two solutions in ##(0^o,360^o)##.

Ray Vickson said:
The book's explanation is poorly worded; it should have said ##\cos(\theta) = 1/3## OR ##\sin(\theta) = 0##. That means that one or the other of those two possibilities can occur, and that corresponds to the existence of more than one solution to the problem in the interval ##0^o < \theta < 360^o##.

If you plot the graphs of ##y = 3\sin(\theta)## and ##y = \tan(\theta)## over the interval ##0^o < \theta < 360^o##, you will see that there are three points where the two graphs cross (five points of crossing if you include ##\theta = 0^o## and ##\theta =360^o##). The equation ##\sin(\theta) = 0## has one solution in ##(0^0,360^o)##, while the equation ##\cos(\theta) = 1/3## has two solutions in ##(0^o,360^o)##.
This is from an alevel past paper
But this explanation is very nice
Thank you very much

## 1. What does "Solve for Sin teta=0" mean?

When a mathematical equation includes the phrase "solve for," it means to find the value of the variable that makes the equation true. In this case, we are looking for the value of the angle teta that, when plugged into the equation Sin teta=0, makes the statement true.

## 2. Why is Sin teta=0 important?

Sin teta=0 is important because it is a key concept in trigonometry, which is the branch of mathematics that deals with the relationships and properties of triangles and the angles within them. Understanding how to solve for Sin teta=0 allows us to solve more complex trigonometric equations and problems.

## 3. How do I solve for Sin teta=0?

To solve for Sin teta=0, we need to find the value of teta that, when plugged into the equation, makes the statement true. This can be done by using a calculator or by using trigonometric identities and properties. For example, we know that Sin 0=0, so teta=0 is one possible solution. However, there are multiple values of teta that could make the equation true, so we need to use additional methods to find all possible solutions.

## 4. What are the steps to solve for Sin teta=0?

The steps to solve for Sin teta=0 will vary depending on the specific equation and problem. However, some general steps may include:
1. Simplify the equation if possible by using trigonometric identities and properties.
2. Determine the possible values of teta that could make the equation true.
3. Check each possible value of teta by plugging it into the equation.
4. If there is more than one possible solution, check for any restrictions or limitations on the values of teta.
5. Write a complete solution that includes all possible values of teta that make the equation true.

## 5. Can I use a calculator to solve for Sin teta=0?

Yes, you can use a calculator to solve for Sin teta=0. Most calculators have a "sin" function that allows you to enter an angle and find its sine value. However, keep in mind that calculators may only give you one possible solution, so it is important to check for any other solutions using other methods as well.

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