What is the general solution for (11)/(sin(90))=(10)/(sin(x)) ?

The general solution for (11)/(sin(90))=(10)/(sin(x)) is x=1.14109…+360n,x=180-1.14109…+360n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(11)/(sin(90))=(10)/(sin(x))

\frac{11}{sin ( 9 0 ^{\circ} )} = \frac{10}{sin ( x )}

x = 1.14109 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.14109 \dots + 36 0^{\circ} n

Radians

x = 1.14109 \dots + 2 πn, x = π - 1.14109 \dots + 2 πn

Solution steps

\frac{11}{sin ( 9 0 ^{\circ} )} = \frac{10}{sin ( x )}

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1

\frac{11}{1} = \frac{10}{sin ( x )}

Cross multiply

\frac{11}{1} = \frac{10}{sin ( x )}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

11 sin (x) = 1 \cdot 10

Simplify

1 \cdot 10 : 10

1 \cdot 10

Multiply the numbers:

1 \cdot 10 = 10

= 10

11 sin (x) = 10

11 sin (x) = 10

Divide both sides by

11

11 sin (x) = 10

Divide both sides by

11

\frac{11 sin ( x )}{11} = \frac{10}{11}

Simplify

sin (x) = \frac{10}{11}

sin (x) = \frac{10}{11}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{10}{sin ( x )}

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{10}{11}

Apply trig inverse properties

sin (x) = \frac{10}{11}

General solutions for

sin (x) = \frac{10}{11}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{10}{11}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{10}{11}) + 36 0^{\circ} n

x = arcsin (\frac{10}{11}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{10}{11}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.14109 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.14109 \dots + 36 0^{\circ} n

2 sec^{2} (x) + 4 tan (x) = 1

8 sin (\frac{3.14}{4 \cdot x}) = 7

cos (3 x) - 21 cos (x) + 16 = 0

sin^{5} (x) - sin (x) = 0

tan (x) = \frac{95.75}{4}

What is the general solution for (11)/(sin(90))=(10)/(sin(x)) ?
The general solution for (11)/(sin(90))=(10)/(sin(x)) is x=1.14109…+360n,x=180-1.14109…+360n