Question 476635: Find all t in the interval [0, 2π] satisfying sin x − cos x = 1. Found 2 solutions by stanbon, Alan3354:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find all t in the interval [0, 2π] satisfying sin x − cos x = 1.
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Square both sides to get:
sin^2 - 2sin*cos + cos^2 = 1
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Since sin^2+cos^2 = 1 you get:
-2sin*cos = 0
sin*cos = 0
Either sin(x) or cos(x) = 0
sin(x) = 0 when x = 0 or pi or 2pi
cos(x) = 0 when x = pi/2 or (3/2)pi
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Cheers,
Stan H.
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You can put this solution on YOUR website! sin(x) - cos(x) = 1
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sin - sqrt(1 - sin^2) = 1
Sub x for sin(x)
x = 1 + sqrt(1 - x^2)
x-1 = sqrt(1 - x^2)
x^2 - 2x + 1 = 1 - x^2
2x^2 - 2x = 0
x = 0, x = 1
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sin(x) = 0 or 1
--> x = 0, x = pi/4
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