Solve each equation for solutions over the interval 0 degree

Solve each equation for solutions over the interval [0 degree, 360 degree). Give solutions to the nearest tenth as appropriate. See Examples 2-5. (cot theta - Squareroot 3)(2sin theta + Squareroot 3) = 0 (tan theta - l)(cos theta - 1) = 0 2 sin theta - 1 = csc theta tan theta + 1 = Squareroot 3 + Squareroot 3 cot theta

Solution

2sin - 1 = csc

==> 2sin - 1 = 1/(sin) ; since csc = 1/(sin)

==> sin [ 2sin - 1] = 1

==> 2sin² - sin = 1

==> 2sin² - sin - 1 = 0

==> sin = [-(-1) + [(-1)² - 4(2)(-1)] / 2(2) ;  [-(-1) - [(-1)² - 4(2)(-1)] / 2(2)

==> sin = [1 + 9] /4 ; [1 - 9]/4

==> sin = 1 , -1/2

==> sin = 1 ; sin = -1/2

==> = /2;   = + /6 , 2 - /6

==> = /2 ; = 7/6 , 11/6

Hence the solutions are = /2 , 7/6 , 11/6

==> = 90^o , 210^o , 330^o