What is the general solution for (sin(82))/(sin(x))=sqrt(5) ?

The general solution for (sin(82))/(sin(x))=sqrt(5) is x=0.45878…+360n,x=180-0.45878…+360n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(sin(82))/(sin(x))=sqrt(5)

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} = 5

x = 0.45878 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.45878 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} = 5

Multiply both sides by

sin (x)

sin (8 2^{\circ}) = 5 sin (x)

Switch sides

5 sin (x) = sin (8 2^{\circ})

Divide both sides by

5

sin (x) = \frac{5 sin ( 8 2 ^{\circ} )}{5}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{5 sin ( 8 2 ^{\circ} )}{5}

Apply trig inverse properties

x = arcsin (\frac{5 sin ( 8 2 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 sin ( 8 2 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.45878 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.45878 \dots + 36 0^{\circ} n

\frac{2 cos ^{2} ( x )}{2 ( 1 - sin ( x ) ) - cos ^{2} ( x )} = 0

2 sin (x) = - 3

tan (θ) = \frac{- 12}{5}, cot (θ)

3 cos (1 x) = - sin (1 x)

0 = 3 cos (θ)

What is the general solution for (sin(82))/(sin(x))=sqrt(5) ?
The general solution for (sin(82))/(sin(x))=sqrt(5) is x=0.45878…+360n,x=180-0.45878…+360n