Fatma A.
asked • 04/29/21Trigonometric equations
1) Find all solutions to the equation 2 sin x + 1 = 0 in the interval [0, 2π].
2) Find all solutions to the equation 3 cos x = 3 in the interval [0, 2π].
3) Find all solutions to the equation 3 sin x − 4 = sin x − 2 in the interval [0, 2π].
4) Find all solutions to the equation tan2 x = 3 in the interval [0, 2π].
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1 Expert Answer
I will work one of these for you.
Then you need to follow the example and work the others for yourself.
It is NOT the job of a tutor to do your homework for you, but to show you how to do it for yourself!
In #1: sin x = -1/2
There are 2 angles which satisfy this equation, one in quadrant 3 and one in quadrant 4---you might like to remember the mnemonic "AllSinTanCos" to tell you which functions are positive in quadrants 1, 2, 3, 4.
The angles are 210 degrees and 330 degrees.
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Duy N.
I'll only do part 1 and you should get the gist of it. 1) 2sin(x)=-1 =sin(x)=-1/2 sine is negative in 3rd and 4th quadrant therefore: x=(π+π/6) or x=(2π-π/6), therefore x=7π/6,11π/6 \04/29/21