What is the general solution for sec(x)=sqrt(4) ?

The general solution for sec(x)=sqrt(4) is x= pi/3+2pin,x=(5pi)/3+2pin

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sec(x)=sqrt(4)

sec (x) = 4

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

sec (x) = 4

Simplify

4 : 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

General solutions for

sec (x) = 2

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

\frac{182.5}{sin ( 36. 6 ^{\circ} )} = \frac{248.6}{sin ( x )}

1 - cos (3 x) = 2 π

(sin (x - 4)) (sin (x - 1)) = 0

θ, r = \frac{10}{3 + 2 cos ( θ )}

sin (x) = \frac{17.75}{42}

What is the general solution for sec(x)=sqrt(4) ?
The general solution for sec(x)=sqrt(4) is x= pi/3+2pin,x=(5pi)/3+2pin