Question textSolve the equation [math: tan⁡(x)−3=0]{ an \left( x ight)-\sqrt{3}=0} over [math: [0,2π]]\displaystyle \Big[0, 2\pi \Big] in radians. Note. Type pi to enter [math: π]\pi and use { , } to enter a set.[input] Check Question 4

Question

Question textSolve the equation [math: tan⁡(x)−3=0]{	an \left( x ight)-\sqrt{3}=0} over [math: [0,2π]]\displaystyle \Big[0, 2\pi \Big] in radians. Note. Type pi to enter [math: π]\pi and use { , } to enter a set.[input] Check Question 4

BlackTom AI · Accepted Answer

We start by identifying the equation provided: tan(x) − sqrt(3) = 0, which is equivalent to tan(x) = sqrt(3).
Next, we recall the general solutions to tan(x) = sqrt(3). The tangent function equals sqrt(3) at an angle of pi/3 in the first quadrant, and since the period of tan is pi, the other solution in [0, 2π) is pi/3 + π = pi/3 + 3.14159265... = 4π/3. 
We must check the interval [0, 2π]. The values pi/3 and 4π/3 lie in this interval, while 0 and 2π are not solutions because tan(0) = 0 and tan(2π) = 0, not sqrt(3).
Therefore, the complete set of solutions within [0, 2π] is {π/3, 4π/3}.
When entering answers, the two blanks should be filled with pi/3 and 4pi/3 respectively, using the notation pi to represent π as instructed.

Question textSolve the equation [math: tan⁡(x)−3=0]{\tan \left( x \right)-\sqrt{3}=0} over [math: [0,2π]]\displaystyle \Big[0, 2\pi \Big] in radians. Note. Type pi to enter [math: π]\pi and use { , } to enter a set.[input] Check Question 4

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