a ∈ [3π/2, 2π]
Cos > 0
sin < 0
sin² a + cos² a = 1
sin² a = 1 - cos² a
sin a = -√(1 - cos² a) = - √(1 - (24/25)²) = - √(25² - 24²)/25 = -√((25 - 24)(25+24))/25 = - 7/25
Cos 2a = cos² a - sin² a = (-7/25)² - (24/25)² = (7 - 24)(7 + 24)/25² = -17*31/25² = - 527/625
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Verified answer
a ∈ [3π/2, 2π]
Cos > 0
sin < 0
sin² a + cos² a = 1
sin² a = 1 - cos² a
sin a = -√(1 - cos² a) = - √(1 - (24/25)²) = - √(25² - 24²)/25 = -√((25 - 24)(25+24))/25 = - 7/25
Cos 2a = cos² a - sin² a = (-7/25)² - (24/25)² = (7 - 24)(7 + 24)/25² = -17*31/25² = - 527/625