What is the general solution for sin(x)*sec(x)=0 ?

The general solution for sin(x)*sec(x)=0 is x=2pin,x=pi+2pin

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sin(x)*sec(x)=0

sin (x) \cdot sec (x) = 0

x = 2 πn, x = π + 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) sec (x) = 0

Solving each part separately

sin (x) = 0 or sec (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

General solutions for

sin (x) = 0

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sec (x) = 0 :

No Solution

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos (x) = - 0.1235, 0 \leq x \leq 2 π

sin (\frac{3 π}{x}) = 0

x, (sin (x) - lo g_{3} (12)) = 20

tan (θ) = - \frac{7}{5}, \frac{π}{2} < θ < π, cos (2 θ)

cos (θ) = - (\frac{1}{2})

What is the general solution for sin(x)*sec(x)=0 ?
The general solution for sin(x)*sec(x)=0 is x=2pin,x=pi+2pin