SOLUTION: Solve the following equations on the interal (0,2π) Exact solutions.
a. Cos²x=1/4
b. sin²x-2sinx-3=0
c. cscx-3cscsecx=0
d. sin(2x)=-cos(2x)
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Question 1043458: Solve the following equations on the interal (0,2π) Exact solutions.
a. Cos²x=1/4
b. sin²x-2sinx-3=0
c. cscx-3cscsecx=0
d. sin(2x)=-cos(2x)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. Cos^2 x=1/4
Cos x= +/- 1/2
This occurs at pi/3. 2pi/3, 4 pi/3, and 5*pi/3
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b.sin^2x-2sin x-3=0
(sin x -3)(sin x+1)=0
sin x cannot equal 3
sin x=-1
That occurs at 3pi/2.
===============
c.csc x-3 csc x sec x=0
csc x(1-3.sec x)=0
csc x cannot equal 0 because 1/sin x cannot equal 0.
Therefore, 1-3 sec x=0
3 sec x=1
sec x=1/3=1/cos x
cos x cannot equal 3. No solution
===============
d. sin (2x)=cos (2x)
sin x=cos x at pi/4, 5 pi/4, 9 pi/4 and 13 pi/4
Therefore, the two are equal at pi/8, 5 pi/8,, 9pi/8 and 13 pi/8
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