SOLUTION: Find all solutions in the interval [0, 2π). sin2x - cos2x = 0

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions in the interval [0, 2π). sin2x - cos2x = 0      Log On


   

Question 769455: Find all solutions in the interval [0, 2π).
sin2x - cos2x = 0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sin%28+2x+%29+-+cos%28+2x+%29+=+0+
+sin%28+2x+%29+=+cos%28+2x+%29+
The sin and cos are equal when:
+2x+=+pi%2F4+
+2x+=+%28+5%2Api+%29%2F4+
-----------------
At an angle of +pi%2F4+,
+sin%28+pi%2F4+%29+=+1%2Fsqrt%282%29+
+cos%28+pi%2F4+%29+=+1%2Fsqrt%282%29+
and
+sin%28+5%2Api%2F4+%29+=+%28-1%29%2Fsqrt%282%29+
+cos%28+5%2Api%2F4+%29+=+%28-1%29%2Fsqrt%282%29+
----------------------------
So, if I say
+2x+=+pi%2F4+
+x+=+pi%2F8+
and
+2x+=+%28+5%2Api+%29%2F4+
+x+=+%28+5%2Api+%29+%2F+8+
------------------
Solutions for +x+ are between ( 0, 2pi ), so
+2x+=+2%2Api+%2B+pi%2F4+
+2x+=+2%2Api+%2B+%285pi%29%2F4+
are solutions also