What is the general solution for sec(x)+sqrt(2)=0,-pi<= x<= (3pi)/2 ?

The general solution for sec(x)+sqrt(2)=0,-pi<= x<= (3pi)/2 is x=(3pi)/4 ,x=(5pi)/4 ,x=-(3pi)/4

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sec(x)+sqrt(2)=0,-pi<= x<= (3pi)/2

sec (x) + 2 = 0, - π \leq x \leq \frac{3 π}{2}

x = \frac{3 π}{4}, x = \frac{5 π}{4}, x = - \frac{3 π}{4}

Degrees

x = 13 5^{\circ}, x = 22 5^{\circ}, x = - 13 5^{\circ}

Solution steps

sec (x) + 2 = 0, - π \leq x \leq \frac{3 π}{2}

Move

2

to the right side

sec (x) + 2 = 0

Subtract

2

from both sides

sec (x) + 2 - 2 = 0 - 2

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{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Solutions for the range

- π \leq x \leq \frac{3 π}{2}

x = \frac{3 π}{4}, x = \frac{5 π}{4}, x = - \frac{3 π}{4}

sin^{2} (x) = \frac{1}{9}

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

tan (x) = 0.327

\frac{cos ( 2 x )}{sin ( x )} = 1

1.04 cos^{2} (θ) + 0.102 cos (θ) - 0.935 = 0

What is the general solution for sec(x)+sqrt(2)=0,-pi<= x<= (3pi)/2 ?
The general solution for sec(x)+sqrt(2)=0,-pi<= x<= (3pi)/2 is x=(3pi)/4 ,x=(5pi)/4 ,x=-(3pi)/4