What is the general solution for 3=1+sec(x) ?

The general solution for 3=1+sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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3=1+sec(x)

3 = 1 + sec (x)

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

3 = 1 + sec (x)

Switch sides

1 + sec (x) = 3

Move

1

to the right side

1 + sec (x) = 3

Subtract

1

from both sides

1 + sec (x) - 1 = 3 - 1

Simplify

sec (x) = 2

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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

3 sin^{2} (x) - 7 sin (x) = 6

2 sin (x) (cos (x) - sin (x)) + (cos (x) - sin (x)) = 0

2 cos^{2} (x) - sin^{2} (x) + 1 = 0

- 6 sin (t) + 6 cos (2 t) = 0

cos^{2} (x) = 4

What is the general solution for 3=1+sec(x) ?
The general solution for 3=1+sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin