InterviewSolution
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If sin x = 3/5, tan y = 1/2 and π/2 < x < π < y < 3π/2 find the value of 8 tan x - √5 sec y. |
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Answer» Given as sin x = 3/5, tan y = 1/2 and π/2 < x< π< y< 3π/2 As we know that, x is in second quadrant and y is in third quadrant. Since, in second quadrant, cos x and tan x are negative. Since, in third quadrant, sec y is negative. On using the formula, cos x = – √(1 - sin2 x) tan x = sin x/cos x Then, cos x = – √(1 - sin2 x) = – √(1 – (3/5)2) = – √(1 – 9/25) = – √((25 - 9)/25) = – √(16/25) = – 4/5 tan x = sin x/cos x = (3/5)/(-4/5) = 3/5 × -5/4 = -3/4 As we know that sec y = – √(1 + tan2 y) = – √(1 + (1/2)2) = – √(1 + 1/4) = – √((4 + 1)/4) = – √(5/4) = – √5/2 Then, 8 tan x – √5 sec y = 8(-3/4) – √5(-√5/2) = -6 + 5/2 = (-12 + 5)/2 = -7/2 Thus, 8 tan x – √5 sec y = -7/2 |
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