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Francesco Paucek

Feb 20, 2025

tan θ = 12/5, π < θ < 3π/2 Find sin (θ/2)?

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tan θ = 12/5 and θ is in III quadrant where sin and cos are negativeopposite side = 12 and adj. side = 5hypotenuse = sqrt(144+25) = 13cos θ = -5/13==> 1 - 2sin^2(θ/2) = -5/132sin^2(θ/2) = 1 + (5/13)= 18/13sin^2(θ/2) = 9/13sin (θ/2) = (3/13)√13... Show More
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tan(t) = -3/4 sec(t)^2 = a million + tan(t)^2 sec(t)^2 = a million + 9/sixteen sec(t)^2 = 25/sixteen cos(t)^2 = sixteen/25 cos(t) = 4/5 sin(t/2) => sqrt((a million - cos(t)) / 2) => sqrt((a million - 4/5) / 2) => sqrt(a million/10) => +/- sqrt(10) / 10 on account that t is in this autumn, then t/2 might properly be the two in Q2 or in this autumn, so the two solutions are valid... Show More
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