What is the general solution for (sin(90))/(3.37)=(sin(x))/(0.7) ?

The general solution for (sin(90))/(3.37)=(sin(x))/(0.7) is x=0.20923…+360n,x=180-0.20923…+360n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(sin(90))/(3.37)=(sin(x))/(0.7)

\frac{sin ( 9 0 ^{\circ} )}{3.37} = \frac{sin ( x )}{0.7}

x = 0.20923 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.20923 \dots + 36 0^{\circ} n

Radians

x = 0.20923 \dots + 2 πn, x = π - 0.20923 \dots + 2 πn

Solution steps

\frac{sin ( 9 0 ^{\circ} )}{3.37} = \frac{sin ( x )}{0.7}

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{1}{3.37} = \frac{sin ( x )}{0.7}

Switch sides

\frac{sin ( x )}{0.7} = \frac{1}{3.37}

Multiply both sides by

0.7

\frac{sin ( x )}{0.7} = \frac{1}{3.37}

Multiply both sides by

0.7

\frac{0.7 sin ( x )}{0.7} = \frac{1 \cdot 0.7}{3.37}

Simplify

\frac{0.7 sin ( x )}{0.7} = \frac{1 \cdot 0.7}{3.37}

Simplify

\frac{0.7 sin ( x )}{0.7} : sin (x)

\frac{0.7 sin ( x )}{0.7}

Cancel the common factor:

0.7

= sin (x)

Simplify

\frac{1 \cdot 0.7}{3.37} : 0.20771 \dots

\frac{1 \cdot 0.7}{3.37}

Multiply the numbers:

1 \cdot 0.7 = 0.7

= \frac{0.7}{3.37}

Divide the numbers:

\frac{0.7}{3.37} = 0.20771 \dots

= 0.20771 \dots

sin (x) = 0.20771 \dots

sin (x) = 0.20771 \dots

sin (x) = 0.20771 \dots

Apply trig inverse properties

sin (x) = 0.20771 \dots

General solutions for

sin (x) = 0.20771 \dots

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

x = arcsin (0.20771 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.20771 \dots) + 36 0^{\circ} n

x = arcsin (0.20771 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.20771 \dots) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.20923 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.20923 \dots + 36 0^{\circ} n

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

7 cos (4 x) = 6

sin (x) tan (x) + 3 tan (x) = 0

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

tan (t) = 2

What is the general solution for (sin(90))/(3.37)=(sin(x))/(0.7) ?
The general solution for (sin(90))/(3.37)=(sin(x))/(0.7) is x=0.20923…+360n,x=180-0.20923…+360n