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

The general solution for sqrt(2)=sec(x) is x= pi/4+2pin,x=(7pi)/4+2pin

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sqrt(2)=sec(x)

2 = sec (x)

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Degrees

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

Solution steps

2 = sec (x)

Switch sides

sec (x) = 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}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

2 csc (θ) - 5 = 0

9 cos^{2} (θ) - 10 cos (θ) - 2 = - 7 cos (θ)

cos (4 x) + 1 = 0

sin (x) = - 2

4 sec (θ) - 5 = 0

What is the general solution for sqrt(2)=sec(x) ?
The general solution for sqrt(2)=sec(x) is x= pi/4+2pin,x=(7pi)/4+2pin