Makes no sense as theta is obviously obtuse

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The discussion centers on solving the equation 12cos(θ - 90) - 8 = 0, leading to the conclusion that sinθ = 2/3. The initial calculation yields θ = 41.8 degrees, which is acute, while a different approach gives θ = 138.2 degrees, indicating an obtuse angle. The confusion arises from the infinite solutions for sinθ = 2/3, prompting questions about other possible angles. Ultimately, the conversation highlights the importance of considering the nature of trigonometric functions when solving for angles.
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Working for a)

Resolving upwards:

12cos(θ -90) - 8 = 0
cos(θ-90) = sinθ
12sinθ = 8
sinθ = 2/3
θ = 41.8 (3.sf)

This makes no sense as theta is obviously obtuse, if I don't simplify to sinθ I get:

cos(θ-90) = 2/3
θ = 48.2... + 90
= 138.2 (1.dp)

Why does it not work if I simplify to sinθ?
 
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sinθ = 2/3 has an infinite number of solutions, what are some others?
 


Villyer said:
sinθ = 2/3 has an infinite number of solutions, what are some others?

180 - θ

silly me, thanks.
 
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