SOLUTION: Find all values of x in the interval [0,2pi] that satisfy the equation sin(2x)=cos x. Enter your answers as a list of numbers separated by commas, e.g. '1,pi/3,4'.

Algebra ->  Trigonometry-basics -> SOLUTION: Find all values of x in the interval [0,2pi] that satisfy the equation sin(2x)=cos x. Enter your answers as a list of numbers separated by commas, e.g. '1,pi/3,4'.       Log On


   

Question 1047009: Find all values of x in the interval [0,2pi] that satisfy the
equation sin(2x)=cos x.
Enter your answers as a list of numbers separated by commas,
e.g. '1,pi/3,4'.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sin%282x%29%7B%7B%7B%22%22=%22%22cos%28x%29

2sin%28x%29cos%28x%29%22%22=%22%22cos%28x%29

2sin%28x%29cos%28x%29-cos%28x%29%22%22=%22%220 

cos%28x%29%282sin%28x%29%5E%22%22-1%29%22%22=%22%220

cos%28x%29%22%22=%22%220,  2sin%28x%29%5E%22%22-1%22%22=%22%220

For the first equation:

x%22%22=%22%22matrix%281%2C3%2Cpi%2F2%2C%22%2C%22%2C3pi%2F2%29

For the second equation:   

2sin%28x%29-1%22%22=%22%220

2sin%28x%29%22%22=%22%221

sin%28x%29%22%22=%22%221%2F2

x%22%22=%22%22matrix%281%2C3%2Cpi%2F6%2C%22%2C%22%2C5pi%2F6%29

Four solutions.

Edwin