If cosθ = -5/13 and 0 <= θ <= 2π, what are possible values of θ?

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In summary, the value of θ in the given equation is unknown and needs to be solved for using inverse trigonometric functions. The range of possible values for θ is between 0 and 2π, and it can be solved using the inverse cosine function or by visualizing with the unit circle. The negative value of cosθ indicates that θ is in the second or third quadrant of the unit circle. There are no other possible values of θ that satisfy the equation.
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Ace.
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Homework Statement



If cosθ = -5/13 and 0 <= θ <= 2π, what are possible values of θ?

Homework Equations



The Attempt at a Solution


θ is in quadrant 2 or 3

in quadrant 2:
related acute = cos[itex]^{-1}[/itex](5/13)
= 1.18
θ = π - 1.18
= 1.96 radians

in quadrant 3:
related acute angle = 1.18
θ = π + 1.18
= 4.32 radians

Those are the two values I got for θ. But my book says the answer is 5.14. Can you tell me where I am going wrong?
 
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  • #2
Where didn't you go wrong?

Nah, I'm just kidding :biggrin: The book's answer is wrong, you're right. They accidentally included the angle in the 4th quadrant rather than the 3rd as you've correctly done.
 

Related to If cosθ = -5/13 and 0 <= θ <= 2π, what are possible values of θ?

1. What is the value of θ in this equation?

The value of θ is unknown and must be solved for using inverse trigonometric functions.

2. What is the range of possible values for θ?

The range of possible values for θ is between 0 and 2π, inclusive.

3. How do you solve for θ?

To solve for θ, you can use the inverse cosine function, which is cos-1. You can also use the unit circle to visualize the possible values of θ.

4. What does the negative value of cosθ indicate?

The negative value of cosθ indicates that the angle θ is in the second or third quadrant of the unit circle.

5. Are there any other possible values of θ?

No, there are no other possible values of θ that satisfy the given equation.

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