Posted by **Sally** on Friday, December 26, 2008 at 3:45am.

Find all the values of x between 0 and 2(pi) for which

sin x + (root 3)cos x = 0

- Maths -
**Damon**, Friday, December 26, 2008 at 9:10am
Whenever you see sines and cosines and sqrt 3, draw a thirty, sixty ninety triangle.

the sin of the 60 degree angle is (sqrt 3)/2

the cosine of the 60 degree angle is 1/2

sqrt(3)/2 = (sqrt 3)(1/2)

Now the quadrants where the sine and cosine have opposite signs are quadrant 2 and quadrant four. So look in those two quadrants.

- Maths -
**Reiny**, Friday, December 26, 2008 at 12:17pm
another not necessarily better approach would be ...

sinx = -√3cosx

tanx = -√3

from the same triangle as Damon's we would get a "basic" angle of 60º or pi/3 radians

but the tan is negative in II or IV, so

x = pi - pi/3 or 2pi - pi/3

or x = 2pi/3 or 5pi/3

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