solve the equation. give a general formula for all the solutions. list all the solutions for ( k = 0,1,2,3,4…

solve the equation. give a general formula for all the solutions. list all the solutions for ( k = 0,1,2,3,4 ), and 5.\n( \tan \theta=\frac{sqrt{3}}{3} )\nwrite the general formula for all the solutions to ( \tan \theta=\frac{sqrt{3}}{3} ).\n( \theta=\frac{pi}{6}+k pi )\n(simplify your answer. use angle measures greater than or equal to 0 and less than ( 2 pi ). type an exact answer, using ( pi ) as needed. use\nlist the solutions for ( k = 0,1,2,3,4 ), and 5.\n( \theta=square )\n(simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression. use a com

solve the equation. give a general formula for all the solutions. list all the solutions for ( k = 0,1,2,3,4 ), and 5.\n( \tan \theta=\frac{sqrt{3}}{3} )\nwrite the general formula for all the solutions to ( \tan \theta=\frac{sqrt{3}}{3} ).\n( \theta=\frac{pi}{6}+k pi )\n(simplify your answer. use angle measures greater than or equal to 0 and less than ( 2 pi ). type an exact answer, using ( pi ) as needed. use\nlist the solutions for ( k = 0,1,2,3,4 ), and 5.\n( \theta=square )\n(simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression. use a com

Answer

Explanation:

Step1: Substitute (k = 0)

Substitute (k = 0) into (\theta=\frac{\pi}{6}+k\pi). (\theta=\frac{\pi}{6}+0\times\pi=\frac{\pi}{6})

Step2: Substitute (k = 1)

Substitute (k = 1) into (\theta=\frac{\pi}{6}+k\pi). (\theta=\frac{\pi}{6}+1\times\pi=\frac{\pi + 6\pi}{6}=\frac{7\pi}{6})

Step3: Substitute (k = 2)

Substitute (k = 2) into (\theta=\frac{\pi}{6}+k\pi). (\theta=\frac{\pi}{6}+2\times\pi=\frac{\pi+12\pi}{6}=\frac{13\pi}{6})

Step4: Substitute (k = 3)

Substitute (k = 3) into (\theta=\frac{\pi}{6}+k\pi). (\theta=\frac{\pi}{6}+3\times\pi=\frac{\pi + 18\pi}{6}=\frac{19\pi}{6})

Step5: Substitute (k = 4)

Substitute (k = 4) into (\theta=\frac{\pi}{6}+k\pi). (\theta=\frac{\pi}{6}+4\times\pi=\frac{\pi+24\pi}{6}=\frac{25\pi}{6})

Step6: Substitute (k = 5)

Substitute (k = 5) into (\theta=\frac{\pi}{6}+k\pi). (\theta=\frac{\pi}{6}+5\times\pi=\frac{\pi+30\pi}{6}=\frac{31\pi}{6})

Answer:

(\frac{\pi}{6},\frac{7\pi}{6},\frac{13\pi}{6},\frac{19\pi}{6},\frac{25\pi}{6},\frac{31\pi}{6})