Asked by Victoria
Determine exact solutions for each equation in the interval x E [0,2 pi]
sin^2x - 3/4 = 0 *3/4 is a fraction
2tan^2x - square root 12 = 0
sin^2x - 3/4 = 0 *3/4 is a fraction
2tan^2x - square root 12 = 0
Answers
Answered by
Reiny
sin^2 x = 3/4
sinx = ±√3/2
I know sin 60° = √3/2 or sin π/3 = √3/2
so x = π/3, 2π/3 , 4π/4 , 5π/3
2 tan^2 x = √12 = 2√3
tan^2 x = √3
now you should know the trig ratios of the 30-60-90 triangle.
once you have the angle in standard position simply locate x in all of the 4 quadrants like I did in the first problem
sinx = ±√3/2
I know sin 60° = √3/2 or sin π/3 = √3/2
so x = π/3, 2π/3 , 4π/4 , 5π/3
2 tan^2 x = √12 = 2√3
tan^2 x = √3
now you should know the trig ratios of the 30-60-90 triangle.
once you have the angle in standard position simply locate x in all of the 4 quadrants like I did in the first problem
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