3cot^2Ɵ-4cscƟ=1 please help

Algebra
Tutor: None Selected Time limit: 1 Day

solve the equation on the interval 0 less than or equal to Ɵ less than or equal to 2π

Nov 23rd, 2014

3cot2Ɵ-4cscƟ=1

3(csc2Ɵ-1)-4 cscƟ=1

3 csc2Ɵ-4 cscƟ= 1+3 =4

Put csc Ɵ = x

3x2-4x-4=0

3x2-6x+2x-4=0

3x(x-2)+2(x-2)=0

(x-2)((3x+2)=0

x= 2 or x = -2/3

csc  Ɵ= 2 or csc Ɵ = -2/3

CSC Ɵ = -2/3 is not permissible since CSC Ɵ > 1 or < -1

CSC Ɵ =2 ;

Sin Ɵ = ½

Ɵ = 300


Nov 23rd, 2014

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Nov 23rd, 2014
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