# Find two solutions for Cosine theta = 1/2 for

• infiniteking1
In summary, the conversation discusses finding two solutions for the equation Cosine theta = 1/2 for 0 degrees less than or equal to theta less than or equal to 360 degrees. One solution is found to be 60 degrees or pi/3 radians, while the other solution is 300 degrees or 5/3 pi radians. The use of reference angles is mentioned and it is clarified that the second solution is actually cos 300° = -0.02209661927868394268907560278956... and not 1/2. The solutions are also provided in both degrees and radians.
infiniteking1
Find two solutions for Cosine theta = 1/2 for...

1. Find two solutions for Cosine theta = 1/2 for 0 degrees less than or equal to theta less than or equal to 360 degrees. Express answers in degrees and radians.

## Homework Equations

3. I know that Cosine theta = 1/2 gives you 60 degrees which is also pie/3 radians. I don't know what the other solution is though. Can anyone help?

Are you familiar with reference angles? See http://www.analyzemath.com/Angle/reference_angle.html" .

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Im familiar with reference angles. I just didnt know to use them but since you mentioned it, what comes to mind is taking 60 degrees from 360 degrees. That leaves me with 300 degrees. From there, i don't know how to proceed.

Well what's cos 300?

yea after a while i figured it out. cos 300= 1/2

No, it's not. cos 300 = -0.02209661927868394268907560278956...

Or perhaps you meant cos 300° = 1/2. The degree sign is important. Without it, I have to assume you mean radians. Speaking of which, don't forget that you were asked to find answers in degrees and radians.

maybe i can help
since cos 60 = 1/2 , i'll use x as theta
=> cos x = cos 60

1. cos x = 60 + k.360
=> x = 60

2. cos theta = -60 + k.360
=> x = 300

in degree x = {60, 300}

## 1. What is the definition of "cosine theta"?

Cosine theta is a mathematical function that represents the ratio of the adjacent side to the hypotenuse in a right triangle. It is commonly used in trigonometry to calculate angles and sides in a triangle.

## 2. How do you solve for cosine theta = 1/2?

To solve for cosine theta = 1/2, you can use the inverse cosine function (arccos) on a calculator or table to find the value of theta. In this case, theta can be either 60 degrees or 300 degrees, as cosine of these angles equals 1/2.

## 3. What are the two solutions for cosine theta = 1/2?

The two solutions for cosine theta = 1/2 are 60 degrees and 300 degrees. This is because cosine of 60 degrees equals 1/2, and so does cosine of 300 degrees.

## 4. Can cosine theta = 1/2 have more than two solutions?

No, cosine theta = 1/2 can only have two solutions. This is because the cosine function is periodic with a period of 360 degrees, meaning that it repeats itself after every 360 degrees. Therefore, any angle that has a cosine value of 1/2 after 360 degrees will have the same solution as the initial angle.

## 5. How can I represent the solutions for cosine theta = 1/2 on a graph?

You can represent the solutions for cosine theta = 1/2 on a graph by plotting the points (60, 1/2) and (300, 1/2) on the unit circle. These points represent the angles 60 degrees and 300 degrees, where the cosine value is 1/2. You can also connect these points to create a line segment, which represents the solutions for cosine theta = 1/2 on the graph.

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