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

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

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3= 3/2 sec(θ)

3 = \frac{3}{2} sec (θ)

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

Degrees

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

Solution steps

3 = \frac{3}{2} sec (θ)

Switch sides

\frac{3}{2} sec (θ) = 3

Multiply both sides by

2

\frac{3}{2} sec (θ) = 3

Multiply both sides by

2

2 \cdot \frac{3}{2} sec (θ) = 3 \cdot 2

Simplify

3 sec (θ) = 6

3 sec (θ) = 6

Divide both sides by

3

3 sec (θ) = 6

Divide both sides by

3

\frac{3 sec ( θ )}{3} = \frac{6}{3}

Simplify

sec (θ) = 2

sec (θ) = 2

General solutions for

sec (θ) = 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}

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

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

tan (θ) = - \frac{2}{3}

sin ((30 t)^{\circ}) = - 0.6

2 cos (2 x) = - 1

sec^{2} (a) cot (a) = 8

6 cos (x) + 2 = 0

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