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

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

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3/2 sec(θ)=3

\frac{3}{2} sec (θ) = 3

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

\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

4 csc (θ) - 3 = 0

2 cos^{2} (θ) - 10 = - cos (θ) - 9

1 = tan (π + c)

6193 cos (x) + 2880 cos (2 x) = 0

sin (x) = \frac{6}{11}

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