What is the general solution for 0=1+4sin(θ) ?

The general solution for 0=1+4sin(θ) is θ=-0.25268…+2pin,θ=pi+0.25268…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

0=1+4sin(θ)

0 = 1 + 4 sin (θ)

θ = - 0.25268 \dots + 2 πn, θ = π + 0.25268 \dots + 2 πn

Degrees

θ = - 14.47751 \dots^{\circ} + 36 0^{\circ} n, θ = 194.47751 \dots^{\circ} + 36 0^{\circ} n

Solution steps

0 = 1 + 4 sin (θ)

Switch sides

1 + 4 sin (θ) = 0

Move

1

to the right side

1 + 4 sin (θ) = 0

Subtract

1

from both sides

1 + 4 sin (θ) - 1 = 0 - 1

Simplify

4 sin (θ) = - 1

4 sin (θ) = - 1

Divide both sides by

4

4 sin (θ) = - 1

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{- 1}{4}

Simplify

sin (θ) = - \frac{1}{4}

sin (θ) = - \frac{1}{4}

Apply trig inverse properties

sin (θ) = - \frac{1}{4}

General solutions for

sin (θ) = - \frac{1}{4}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

θ = arcsin (- \frac{1}{4}) + 2 πn, θ = π + arcsin (\frac{1}{4}) + 2 πn

θ = arcsin (- \frac{1}{4}) + 2 πn, θ = π + arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

θ = - 0.25268 \dots + 2 πn, θ = π + 0.25268 \dots + 2 πn

x, u = cos (x^{2} y)

6 sin^{2} (x) - sin (x) cos (x) - 2 cos^{2} (x) = 0

tan (θ) = \frac{20 ( 9.8 )}{25}

t, 0 = 8 sin (\frac{π t}{12}) + 32

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

What is the general solution for 0=1+4sin(θ) ?
The general solution for 0=1+4sin(θ) is θ=-0.25268…+2pin,θ=pi+0.25268…+2pin