What is the general solution for sin(θ)= 1/3 ?

The general solution for sin(θ)= 1/3 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(θ)= 1/3

sin (θ) = \frac{1}{3}

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

Degrees

θ = 19.47122 \dots^{\circ} + 36 0^{\circ} n, θ = 160.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{1}{3}

Apply trig inverse properties

sin (θ) = \frac{1}{3}

General solutions for

sin (θ) = \frac{1}{3}

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

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

cos (θ) = \frac{1}{2}

tan (2 x) = 3 tan (x)

tan (2 θ) = - 1

sin (x) - cos (x) = 1

cos^{2} (x) = \frac{3}{4}

What is the general solution for sin(θ)= 1/3 ?
The general solution for sin(θ)= 1/3 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin