SOLUTION: Can you please help me solve this equation: {{{ sin(x+1)=cos(x) }}} with answers between 0 and 2pi?

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please help me solve this equation: {{{ sin(x+1)=cos(x) }}} with answers between 0 and 2pi?      Log On


   

Question 1075988: Can you please help me solve this equation: +sin%28x%2B1%29=cos%28x%29+ with answers between 0 and 2pi?
Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
.
Can you please help me solve this equation: +sin%28x%2B1%29=cos%28x%29+ with answers between 0 and 2pi?
~~~~~~~~~~~~~~~~~~~~~~~ 

sin(x+1) = cos(x)  <---->  sin%28x%2B1%29 = sin%28pi%2F2+-+x%29  


This equation has TWO roots in the area of interest:

1)  x+1 = pi%2F2-x  ---->  2x = pi%2F2+-1  <---->  x = %281%2F2%29%2A%28pi%2F2-1%29,

     and 

2)  x+1 = pi%2F2-x+%2B+2%2Api  ---->  2x = pi%2F2+-1+%2B+2pi  <---->  x = %281%2F2%29%2A%28pi%2F2-1%29 + pi%29.

Answer. The solutions are x = %281%2F2%29%2A%28pi%2F2-1%29 and x = %281%2F2%29%2A%28pi%2F2-1%29 + pi%29.




Plots y = sin(x+1) (red) and y = cos(x) (green)


The plot shows two roots in the interval [0, 2pi).

Solved.