How do you solve sqrt3cscx-2=0?

1 Answer
Sep 5, 2015

{x | x = pi/3 + 2kpi or x = (2pi)/3 + 2kpi, k in ZZ}

Explanation:

To solve this equation, we need to isolate x, which means isolating the trigonometric function that has x in it.
If you find it hard to remember the unit circle values for secant or cosecant, you can always use the more familiar sine and cosine functions:

sqrt(3)csc(x) - 2 = 0

sqrt(3)*1/sin(x) - 2 = 0

sqrt(3)*1/sin(x) = 2

sqrt(3) = 2sin(x)

sqrt(3)/2 = sin(x)

The values for x where sqrt(3)/2 = sin(x) are pi/3 and (2pi)/3 radians.

Since there's no specified domain in the problem, the answer is the general solution.
The sin function has the period 2pi, pi/3 and (2pi)/3 repeat every 2pi in the answer.

{x | x = pi/3 + 2kpi or x = (2pi)/3 + 2kpi, k in ZZ}