What is the general solution for sec(x)=(2sqrt(3))/2 ?

The general solution for sec(x)=(2sqrt(3))/2 is x=0.95531…+2pin,x=2pi-0.95531…+2pin

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sec(x)=(2sqrt(3))/2

sec (x) = \frac{2 3}{2}

x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn

Degrees

x = 54.73561 \dots^{\circ} + 36 0^{\circ} n, x = 305.26438 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sec (x) = \frac{2 3}{2}

Divide the numbers:

\frac{2}{2} = 1

sec (x) = 3

Apply trig inverse properties

sec (x) = 3

General solutions for

sec (x) = 3

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

Show solutions in decimal form

x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn

6 sin (2 x) = 4

cos^{2} (x) + sin (x) = - 1

sin (a) = \frac{2}{3}

2 sin (2 x) + 3 sin (x) = 0

sin (x) = - \frac{2}{5}

What is the general solution for sec(x)=(2sqrt(3))/2 ?
The general solution for sec(x)=(2sqrt(3))/2 is x=0.95531…+2pin,x=2pi-0.95531…+2pin