SOLUTION: Solve the following equations given that 0° &#8804; &#952; < 360° : A) 3 tan 3&#952; - sqrt(3) = 0 B) 3 csc &#952;/2 - 2 sqrt(3) = 0 Thanks

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following equations given that 0° &#8804; &#952; < 360° : A) 3 tan 3&#952; - sqrt(3) = 0 B) 3 csc &#952;/2 - 2 sqrt(3) = 0 Thanks      Log On


   

Question 967283: Solve the following equations given that 0° ≤ θ < 360° :
A) 3 tan 3θ - sqrt(3) = 0
B) 3 csc θ/2 - 2 sqrt(3) = 0
Thanks
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!

A) 3.tan%283%2Atheta%29 - sqrt%283%29 = 0,

      tan%283%2Atheta%29 = sqrt%283%29%2F3 = 1%2Fsqrt%283%29,

      3%2Atheta = 30°  or  180° + 30° = 210°,

      theta = 10°  or  210%2F3 = 70°.


B) 3.csc+%28theta%2F2%29 - 2.sqrt%283%29 = 0,

      1%2Fsin%28theta%2F2%29 = 2%2Fsqrt%283%29,

      sin%28theta%2F2%29 = sqrt%283%29%2F2,

      theta%2F2 = 60°  or  120°,

      theta = 120°  or  240°.