Asked by Thomas
Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
cos(x+3pi/4) - cos(x-3pi/4) = 1
cos(x+3pi/4) - cos(x-3pi/4) = 1
Answers
Answered by
amy felton
right
Answered by
Reiny
cos(x+3pi/4) = cosx cos(3π/4) - sinx sin(3π/4)
cos(x - (3π/4)) = cosx cos(3π/4) + sinx sin(3π/4)
cos(x+3pi/4) - cos(x-3pi/4) = 1
cosx cos(3π/4) - sinx sin(3π/4) - cosx cos(3π/4) - sinx sin(3π/4) = 1
-2sinx sin(3π/4) = 1
sinx (√2/2) = -1/2
sinx = (-1/2)(2/√2) = -1/√2
x = 225° or x = 315°
x = 5π/4 or x = 7π/4
cos(x - (3π/4)) = cosx cos(3π/4) + sinx sin(3π/4)
cos(x+3pi/4) - cos(x-3pi/4) = 1
cosx cos(3π/4) - sinx sin(3π/4) - cosx cos(3π/4) - sinx sin(3π/4) = 1
-2sinx sin(3π/4) = 1
sinx (√2/2) = -1/2
sinx = (-1/2)(2/√2) = -1/√2
x = 225° or x = 315°
x = 5π/4 or x = 7π/4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.