What is the general solution for 1/(e^{sin(x))}=1 ?

The general solution for 1/(e^{sin(x))}=1 is x=2pin,x=pi+2pin

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Popular >

1/(e^{sin(x))}=1

Solution

\frac{1}{e ^{s i n (x)}} = 1

Solution

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

\frac{1}{e ^{s i n (x)}} = 1

Apply exponent rules

\frac{1}{e ^{s i n (x)}} = 1

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{e ^{s i n (x)}} = e^{- s i n (x)}

e^{- s i n (x)} = 1

f (x) = g (x)

, then

ln (f (x)) = ln (g (x))

ln (e^{- s i n (x)}) = ln (1)

Apply log rule:

ln (e^{a}) = a

ln (e^{- s i n (x)}) = - sin (x)

- sin (x) = ln (1)

- sin (x) = ln (1)

Solve

- sin (x) = ln (1) : sin (x) = 0

- sin (x) = ln (1)

Divide both sides by

- 1

- sin (x) = ln (1)

Divide both sides by

- 1

\frac{- sin ( x )}{- 1} = \frac{ln ( 1 )}{- 1}

Simplify

\frac{- sin ( x )}{- 1} = \frac{ln ( 1 )}{- 1}

Simplify

\frac{- sin ( x )}{- 1} : sin (x)

\frac{- sin ( x )}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

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

Apply rule

\frac{a}{1} = a

= sin (x)

Simplify

\frac{ln ( 1 )}{- 1} : 0

\frac{ln ( 1 )}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{ln ( 1 )}{1}

Apply rule

\frac{a}{1} = a

= - ln (1)

Apply log rule:

lo g_{a} (1) = 0

= - 0

= 0

sin (x) = 0

sin (x) = 0

sin (x) = 0

sin (x) = 0

Verify Solutions:

sin (x) = 0

True

Check the solutions by plugging them into

\frac{1}{e ^{s i n (x)}} = 1

Remove the ones that don't agree with the equation.

Plug in

sin (x) = 0 :

True

\frac{1}{e ^{0}} = 1

\frac{1}{e ^{0}} = 1

\frac{1}{e ^{0}}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= \frac{1}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 1

1 = 1

True

The solution is

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

Popular Examples

|cos(x)|=(sqrt(3))/2

∣ cos (x) ∣ = \frac{3}{2}

tan(θ)=(-1)/(sqrt(3)),0<= θ<= 360

tan (θ) = \frac{- 1}{3}, 0^{\circ} \leq θ \leq 36 0^{\circ}

4cos(pi/4 (x+3))=0

4 cos (\frac{π}{4} (x + 3)) = 0

sin^3(x)=cos(x)

sin^{3} (x) = cos (x)

tan((91pi)/(36))=cos(360-x)

tan (\frac{91 π}{36}) = cos (36 0^{\circ} - x)

Frequently Asked Questions (FAQ)

What is the general solution for 1/(e^{sin(x))}=1 ?
The general solution for 1/(e^{sin(x))}=1 is x=2pin,x=pi+2pin