tranquility
New member
- Joined
- Oct 3, 2010
- Messages
- 2
Hey. I find these triginometry equations so annoying. Once I find the solution it is so obvious and I usually make stupid mistakes halfway through. My question is:
By expressing the equation in terms of sin x and cos x, find all values of x, for 0 < x < 360, which satisfy the equation:
1 + cos 2x = 4 sin 2x
I have tried expanding the cos2x and the sin 2x using the multiple angle formulas but I get a bit stuck. This is what I have tried so far.
1 + cos 2x = 4 (2sinxcosx)
1 + (1-2sin^2x) = 8sinxcosx
2 - 2sin^2x = 8sinxcosx
2 - 2 (1 - cos^2x) = 8sinxcosx
2 - 2 + 2cos^2x = 8sinxcosx
2 cos ^2x - 8sinxcosx = 0
cosx (2cosx - 8sinx)
cos x = 0 2cosx-8sinx = 0 ?????
x = cos^-1 (0) = 90
^^ I've got this answer right but what about the other equation gahh.
The final answers are: x = 90, 270, 14, 194
How do I get to the buggers? If you could please point out where I've gone wrong / what I could have done differentl.
Thank you everyone
By expressing the equation in terms of sin x and cos x, find all values of x, for 0 < x < 360, which satisfy the equation:
1 + cos 2x = 4 sin 2x
I have tried expanding the cos2x and the sin 2x using the multiple angle formulas but I get a bit stuck. This is what I have tried so far.
1 + cos 2x = 4 (2sinxcosx)
1 + (1-2sin^2x) = 8sinxcosx
2 - 2sin^2x = 8sinxcosx
2 - 2 (1 - cos^2x) = 8sinxcosx
2 - 2 + 2cos^2x = 8sinxcosx
2 cos ^2x - 8sinxcosx = 0
cosx (2cosx - 8sinx)
cos x = 0 2cosx-8sinx = 0 ?????
x = cos^-1 (0) = 90
^^ I've got this answer right but what about the other equation gahh.
The final answers are: x = 90, 270, 14, 194
How do I get to the buggers? If you could please point out where I've gone wrong / what I could have done differentl.
Thank you everyone