What is the general solution for 7sin(θ)-1=5sin(θ) ?

The general solution for 7sin(θ)-1=5sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

7sin(θ)-1=5sin(θ)

7 sin (θ) - 1 = 5 sin (θ)

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

7 sin (θ) - 1 = 5 sin (θ)

Solve by substitution

7 sin (θ) - 1 = 5 sin (θ)

Let:

sin (θ) = u

7 u - 1 = 5 u

7 u - 1 = 5 u : u = \frac{1}{2}

7 u - 1 = 5 u

Move

1

to the right side

7 u - 1 = 5 u

Add

1

to both sides

7 u - 1 + 1 = 5 u + 1

Simplify

7 u = 5 u + 1

7 u = 5 u + 1

Move

5 u

to the left side

7 u = 5 u + 1

Subtract

5 u

from both sides

7 u - 5 u = 5 u + 1 - 5 u

Simplify

2 u = 1

2 u = 1

Divide both sides by

2

2 u = 1

Divide both sides by

2

\frac{2 u}{2} = \frac{1}{2}

Simplify

u = \frac{1}{2}

u = \frac{1}{2}

Substitute back

u = sin (θ)

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (θ) = \frac{1}{2}

General solutions for

sin (θ) = \frac{1}{2}

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}

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

csc (θ) = - \frac{7}{3}

sin (θ) = \frac{5}{8}

arctan (2 x) + arctan (x) = \frac{π}{4}

tan (a) = 1

cos (2 θ) = 2, cos^{2} (θ) - 1 = 2, (- \frac{3}{5})^{2} - 1 = - \frac{7}{25}

What is the general solution for 7sin(θ)-1=5sin(θ) ?
The general solution for 7sin(θ)-1=5sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin