Sinx+root3cos=1 if 0<=x<360
3 answers
Root3cosx nt root3cos
If you meant
sinx + √3 cosx = 1
then try this
√3 cosx = 1-sinx
3cos^2x = 1-2sinx+sin^2x
3(1-sin^2x) = 1-2sinx+sin^2x
4sin^2x - 2sinx - 2 = 0
2(2sinx+1)(sinx-1) = 0
sinx = -1/2 or 1
x = 90 or 210 or 330
But 210 does not work in the original equation, so throw it out.
sinx + √3 cosx = 1
then try this
√3 cosx = 1-sinx
3cos^2x = 1-2sinx+sin^2x
3(1-sin^2x) = 1-2sinx+sin^2x
4sin^2x - 2sinx - 2 = 0
2(2sinx+1)(sinx-1) = 0
sinx = -1/2 or 1
x = 90 or 210 or 330
But 210 does not work in the original equation, so throw it out.
sinx+1.732cosx=1
2(sinx(1/2)+(1.732/2)cosx)=1
sin(x+pi/3)=1/2
x+pi/3=5pi/6
x=3pi/2
2(sinx(1/2)+(1.732/2)cosx)=1
sin(x+pi/3)=1/2
x+pi/3=5pi/6
x=3pi/2
3 answers