SOLUTION: find all t in the interval [0,2pi] satisfying sin x - cos x = 1. I do not know where to start with this

Algebra ->  Trigonometry-basics -> SOLUTION: find all t in the interval [0,2pi] satisfying sin x - cos x = 1. I do not know where to start with this      Log On


   

Question 328059: find all t in the interval [0,2pi] satisfying sin x - cos x = 1. I do not know where to start with this
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the trig identitites along with your equation.
sin%28x%29-cos%28x%29=1
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sin%28x%29=cos%28x%29%2B1
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sin%5E2%28x%29=%28cos%28x%29%2B1%29%5E2
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1-cos%5E2%28x%29=cos%5E2%28x%29%2B2cos%28x%29%2B1
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2cos%5E2%28x%29%2B2cos%28x%29=0
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cos%28x%29%28cos%28x%29%2B1%29=0
Two solutions from the zero product property:
cos%28x%29=0
x=pi%2F2 and x=%283pi%29%2F2
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cos%28x%29%2B1=0
cos%28x%29=-1
x=pi
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Verify the solutions.
sin%28x%29-cos%28x%29=1
sin%28pi%29-cos%28pi%29=1
0-%28-1%29=1
1=1
x=pi is a valid solution.
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sin%28x%29-cos%28x%29=1
sin%28pi%2F2%29-cos%28pi%2F2%29=1
1-0=1
1=1
x=pi%2F2 is a valid solution.
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sin%28x%29-cos%28x%29=1
sin%28%283pi%29%2F2%29-cos%28%283pi%29%2F2%29=1
-1-0=1
-1=1
x=%283pi%29%2F2 is not a valid solution.
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Two solution: x=pi%2F2 and x=pi
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