Find theta given known cos and sin....

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The discussion revolves around finding the angle theta (θ) given the cosine and sine values. Participants clarify that the angle must be in the fourth quadrant due to the positive cosine and negative sine. There is confusion regarding the calculation of 2θ, with some asserting it can exceed 2π, leading to various interpretations of the angle's value. The importance of adhering to the specified range for θ is emphasized, and the distinction between angles in different quadrants is discussed. Ultimately, the conversation highlights the complexities of trigonometric identities and angle restrictions in solving such problems.
  • #31
Helly123 said:
X (theta) must be on 4 Quadrant, so 2x must on 8 quadrants, 540<2x<=720
X 1=5/4 π
X2 = 7/4 π
Both added 2π to get x at 8 quadrants
X1 = 13/4 π
X2 = 15/4 π

Both satisfied the domain
How to decide which one is the answer?
Those actually should written be something like
2x1 = (5/4) π
2x2 = (7/4) π​
Then adding 2π gives (two new possibilities for x):
2x3 = (13/4) π
2x4 = (15/4) π​

Solve for each xk .
 
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