Find the exact values of s in the interval 2 pi pi that sat

Find the exact values of s in the interval [- 2 pi, pi) that satisfy the given condition 3 tan^2 s = 1. s = (Use a comma to separate answers as needed. Simplify your answer. Type exact answers, using pi as needed. Use integers or fractions for any numbers in the expression.)

Solution

Solution:

=> 3tan²(s) = 1
=> tan²(s) = 1/3
=> tan(s) = +/- 1/3   (we know tan(30°) = 1/3 = tan(pi/6))
s = -11pi/6, -7pi/6, -5pi/6, -pi/6, pi/6, 5pi/6 in interval [-2pi, pi)