Asked by Abe
Write an expression that gives all solutions to the equation
sin x + cos x = - radical 2
sin x + cos x = - radical 2
Answers
Answered by
drwls
Square both sides. The answer we get for sin x + cos x may have the wrong sign, so we will have to chaeck that later.
sin^2 x + cos^2x + 2 sinx cosx = 2
1 + sin(2x) = 2
sin (2x) = 1
2x = pi/2 + 2 n pi where n is any integer
x = pi/4 + n pi
= pi/4, 5 pi/4
= 45 , 225 degrees
The first answer does not work because the sign is wrong, so the only answer between 0 and 360 degrees is 225 degees
sin^2 x + cos^2x + 2 sinx cosx = 2
1 + sin(2x) = 2
sin (2x) = 1
2x = pi/2 + 2 n pi where n is any integer
x = pi/4 + n pi
= pi/4, 5 pi/4
= 45 , 225 degrees
The first answer does not work because the sign is wrong, so the only answer between 0 and 360 degrees is 225 degees
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.