Find Radian Angle: Value of cos θ = -1/2, π ≤ θ ≤ 2π

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In summary, to find the radian value of θ in the given range with a cosine of -1/2, you can use the inverse cosine function and get the first value of (2π)/3. To find the second value, you can use basic geometry and the unit circle to determine that the angle in the third quadrant with a cosine of -1/2 is (4π)/3.
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Veronica_Oles
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Homework Statement


For the value of cos θ, determine the radian value of θ if π ≤ θ ≤ 2π.

Value is -1/2.

Homework Equations

The Attempt at a Solution


I got the first value which is cos-1(-1/2) which I got (2π)/3.
However I am unsure how to get the second value.
I thought that since the first value is in second quadrant the other value is in the third quadrant, then I would take θ-π to find my value in the quadrant. But my answer was incorrect. Can someone pls guide me? Thx.
 
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Veronica_Oles said:

Homework Statement


For the value of cos θ, determine the radian value of θ if π ≤ θ ≤ 2π.

Value is -1/2.

Homework Equations

The Attempt at a Solution


I got the first value which is cos-1(-1/2) which I got (2π)/3.
However I am unsure how to get the second value.
I thought that since the first value is in second quadrant the other value is in the third quadrant, then I would take θ-π to find my value in the quadrant. But my answer was incorrect. Can someone pls guide me? Thx.
What angle in the 3rd quadrant has a cosine of -1/2? Draw a unit circle and use basic geometry to find that angle.
 
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FAQ: Find Radian Angle: Value of cos θ = -1/2, π ≤ θ ≤ 2π

What is a radian angle?

A radian angle is a unit of measurement used to express angles in the metric system. It is defined as the angle that subtends an arc of length equal to the radius of the circle.

How do I find the value of cos θ?

To find the value of cos θ, you can use a scientific calculator or a trigonometric table. Alternatively, you can use the inverse cosine function (cos^-1) to find the angle θ that has the given cosine value.

What does cos θ = -1/2 mean?

In this context, cos θ = -1/2 means that the cosine of the angle θ is equal to -1/2. This can also be written as cos θ = -0.5. It is a mathematical equation that helps us find the value of the angle θ.

What is the range of values for θ in this equation?

The given equation, cos θ = -1/2, has a specific range of values for θ. In this case, the angle θ can take on any value between π (pi) radians and 2π (2 times pi) radians, including both π and 2π.

How can I use this information in real-life applications?

The concept of finding the radian angle using the cosine value has many practical applications in fields such as physics, engineering, and navigation. For example, it can be used to calculate distances and angles in a triangle or to determine the position of an object in space based on its coordinates.

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