What is the general solution for -3/2 =-1/2 sec(x) ?

The general solution for -3/2 =-1/2 sec(x) is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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-3/2 =-1/2 sec(x)

- \frac{3}{2} = - \frac{1}{2} sec (x)

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Degrees

x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- \frac{3}{2} = - \frac{1}{2} sec (x)

Switch sides

- \frac{1}{2} sec (x) = - \frac{3}{2}

Multiply both sides by

- 2

- \frac{1}{2} sec (x) = - \frac{3}{2}

Multiply both sides by

- 2

(- \frac{1}{2} sec (x)) (- 2) = (- \frac{3}{2}) (- 2)

Simplify

(- \frac{1}{2} sec (x)) (- 2) = (- \frac{3}{2}) (- 2)

Simplify

(- \frac{1}{2} sec (x)) (- 2) : sec (x)

(- \frac{1}{2} sec (x)) (- 2)

Remove parentheses:

(- a) = - a, - (- a) = a

= \frac{1}{2} sec (x) \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2} sec (x)

Cancel the common factor:

2

= sec (x) \cdot 1

Multiply:

sec (x) \cdot 1 = sec (x)

= sec (x)

Simplify

(- \frac{3}{2}) (- 2) : 3

(- \frac{3}{2}) (- 2)

Remove parentheses:

(- a) = - a, - (- a) = a

= \frac{3}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 2}{2}

Cancel the common factor:

2

= 3

sec (x) = 3

sec (x) = 3

sec (x) = 3

Apply trig inverse properties

sec (x) = 3

General solutions for

sec (x) = 3

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

sin (3 x + 1) = \frac{1}{2}

cos (x) = \frac{1 3 ^{2} + 1 8 ^{2} - 2 8 ^{2}}{2 \cdot 13 \cdot 18}

0.16085 = sin (\frac{2 π}{365} (x - 114))

sin (x) = - \frac{8}{17}, π \leq x \leq \frac{3 π}{2}, sin (2 x)

tan (θ) cos (2 7^{\circ}) = cos (6 3^{\circ})

What is the general solution for -3/2 =-1/2 sec(x) ?
The general solution for -3/2 =-1/2 sec(x) is x=1.23095…+2pin,x=2pi-1.23095…+2pin