What is the general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) ?

The general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) is θ=1.57079…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin((4pi)/(11))=sin(θ)*sin((7pi)/(11))

sin (\frac{4 π}{11}) = sin (θ) \cdot sin (\frac{7 π}{11})

θ = 1.57079 \dots + 2 πn

Degrees

θ = 89.99999 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (\frac{4 π}{11}) = sin (θ) sin (\frac{7 π}{11})

Switch sides

sin (θ) sin (\frac{7 π}{11}) = sin (\frac{4 π}{11})

Divide both sides by

sin (\frac{7 π}{11})

sin (θ) sin (\frac{7 π}{11}) = sin (\frac{4 π}{11})

Divide both sides by

sin (\frac{7 π}{11})

\frac{sin ( θ ) sin ( \frac{7 π}{11} )}{sin ( \frac{7 π}{11} )} = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

Simplify

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

Apply trig inverse properties

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

General solutions for

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

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

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn, θ = π - arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn, θ = π - arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

Merge Overlapping Intervals

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

Show solutions in decimal form

θ = 1.57079 \dots + 2 πn

sin (2 x) = 2 tan (2 x)

- 2 cos (2 θ) + 12 = 4 sin (θ) + 9

sec^{2} (x) + sec (x) - 2 = 0

(cot (x) - 1) (2 sin (x) + 1) = 0

y, x = tan (y)

What is the general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) ?
The general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) is θ=1.57079…+2pin