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

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

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3/2 sec(x)=3

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

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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

3 sec (x) = 6

3 sec (x) = 6

Divide both sides by

3

3 sec (x) = 6

Divide both sides by

3

\frac{3 sec ( x )}{3} = \frac{6}{3}

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

9 (cos (a))^{2} - 9 (sin (a))^{2} = 0

1 - 2 cos^{2} (x) = 0, 0 \leq x \leq 2 π

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

9.2 cos (x) = 6.3

sec (x) + 3 tan (x) = 1 + 2 tan (x)

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