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trig identities question - please help ive bin stuck for hours on it
Solve the equation in the interval 0<x<2pi. give answer in radians.
3cos^2x - 5sinxcosx - 2sin^2x = 0
The ^2 indicates superscript and is read as eg. 3 cosine x squared
Im finding it hard to rearrange the equation into a form from which i can deduce the values of x. I expect that the use of trigonometric identities are needed to do this or maybe dividing throughout by a term - im so stuck please help me
3cos^2x - 5sinxcosx - 2sin^2x = 0
The ^2 indicates superscript and is read as eg. 3 cosine x squared
Im finding it hard to rearrange the equation into a form from which i can deduce the values of x. I expect that the use of trigonometric identities are needed to do this or maybe dividing throughout by a term - im so stuck please help me
ryan750
Solve the equation in the interval 0<x<2pi. give answer in radians.
3cos^2x - 5sinxcosx - 2sin^2x = 0
The ^2 indicates superscript and is read as eg. 3 cosine x squared
Im finding it hard to rearrange the equation into a form from which i can deduce the values of x. I expect that the use of trigonometric identities are needed to do this or maybe dividing throughout by a term - im so stuck please help me
3cos^2x - 5sinxcosx - 2sin^2x = 0
The ^2 indicates superscript and is read as eg. 3 cosine x squared
Im finding it hard to rearrange the equation into a form from which i can deduce the values of x. I expect that the use of trigonometric identities are needed to do this or maybe dividing throughout by a term - im so stuck please help me
Factorise to
(3cosx +sinx)(cosx - 2sinx)
then take content of each bracket, divide by cos to get tans
Aitch
ryan750
Solve the equation in the interval 0<x<2pi. give answer in radians.
3cos^2x - 5sinxcosx - 2sin^2x = 0
The ^2 indicates superscript and is read as eg. 3 cosine x squared
Im finding it hard to rearrange the equation into a form from which i can deduce the values of x. I expect that the use of trigonometric identities are needed to do this or maybe dividing throughout by a term - im so stuck please help me
3cos^2x - 5sinxcosx - 2sin^2x = 0
The ^2 indicates superscript and is read as eg. 3 cosine x squared
Im finding it hard to rearrange the equation into a form from which i can deduce the values of x. I expect that the use of trigonometric identities are needed to do this or maybe dividing throughout by a term - im so stuck please help me
3cos²x - 5sinxcosx - 2sin²x = 0
6cos²x - 10sinxcosx - 4sin²x = 0
cos2x = 1 - 2sin²x
2sin²x = 1 - cos2x
4sin²x = 2 - 2cos2x
sin2x = sin(x+x) = sinxcosx + cosxsinx = 2sinxcosx
5sin2x = 10sinxcosx
cos2x = 2cos²x - 1
2cos²x = cos2x + 1
6cos²x = 3cos2x + 3
6cos²x - 10sinxcosx - 4sin²x = 0
substituting in the bold values, and calling θ = 2x
(3cos2x + 3) - (5sin2x) - (2 - 2cos2x) = 0
3cosθ + 3 - 5sinθ - 2 + 2cosθ = 0
5cosθ - 5sinθ + 1 = 0
5(cosθ - sinθ
= -1cosθ - sinθ = -1/5
now cosθ - sinθ = √2[cos(θ+pi/4)]
√2[cos(θ+pi/4)] = -1/5
cos(θ+pi/4) = -1/(5√2)
the conditions are 0<x<2pi, so 0 < (θ/2) < 2pi and 0 < θ < 4pi, and pi/4 < θ+pi/4 < 4pi + pi/4 = 17pi/4
θ + pi/4 = 1.71, 4.57, 7.99, 10.85
θ = 0.92, 3.78, 7.20, 10.07
x = 0.46, 1.89, 3.60, 5.04
all to 2 decimal places. god... I hope that's right, I spent quite a while on all that...
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