I'm trying to learn the material so if u could explain the steps that would be great thanks!
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cot(θ) = cos(θ)/sin(θ). 12/13 > 0 and cos(θ) > 0 so sin(θ) must be positive too.
Use the trig identity cot²(θ) + 1 = csc²(θ):
(12/13)² + 1 = 1/sin²(θ)
313/169 = 1/sin²(θ)
169/313 = sin²(θ)
±√(169/313) = sin(θ)
±13√313 / 313 = sin(θ)
But we've determined that sin(θ) > 0 so sin(θ) = 13 √313 / 313
Use the trig identity cot²(θ) + 1 = csc²(θ):
(12/13)² + 1 = 1/sin²(θ)
313/169 = 1/sin²(θ)
169/313 = sin²(θ)
±√(169/313) = sin(θ)
±13√313 / 313 = sin(θ)
But we've determined that sin(θ) > 0 so sin(θ) = 13 √313 / 313
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