What is the general solution for (sin(97))/(14)=(sin(b))/(10) ?

The general solution for (sin(97))/(14)=(sin(b))/(10) is b=0.78802…+360n,b=180-0.78802…+360n

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(sin(97))/(14)=(sin(b))/(10)

\frac{sin ( 9 7 ^{\circ} )}{14} = \frac{sin ( b )}{10}

b = 0.78802 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.78802 \dots + 36 0^{\circ} n

Radians

b = 0.78802 \dots + 2 πn, b = π - 0.78802 \dots + 2 πn

Solution steps

\frac{sin ( 9 7 ^{\circ} )}{14} = \frac{sin ( b )}{10}

Switch sides

\frac{sin ( b )}{10} = \frac{sin ( 9 7 ^{\circ} )}{14}

Multiply both sides by

10

\frac{sin ( b )}{10} = \frac{sin ( 9 7 ^{\circ} )}{14}

Multiply both sides by

10

\frac{sin ( b )}{10} \cdot 10 = \frac{sin ( 9 7 ^{\circ} )}{14} \cdot 10

Simplify

\frac{sin ( b )}{10} \cdot 10 = \frac{sin ( 9 7 ^{\circ} )}{14} \cdot 10

Simplify

\frac{sin ( b )}{10} \cdot 10 : sin (b)

\frac{sin ( b )}{10} \cdot 10

Multiply fractions:

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

= \frac{sin ( b ) \cdot 10}{10}

Cancel the common factor:

10

= sin (b)

Simplify

\frac{sin ( 9 7 ^{\circ} )}{14} \cdot 10 : \frac{5 sin ( 9 7 ^{\circ} )}{7}

\frac{sin ( 9 7 ^{\circ} )}{14} \cdot 10

Multiply fractions:

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

= \frac{sin ( 9 7 ^{\circ} ) \cdot 10}{14}

Cancel the common factor:

2

= \frac{5 sin ( 9 7 ^{\circ} )}{7}

sin (b) = \frac{5 sin ( 9 7 ^{\circ} )}{7}

sin (b) = \frac{5 sin ( 9 7 ^{\circ} )}{7}

sin (b) = \frac{5 sin ( 9 7 ^{\circ} )}{7}

Apply trig inverse properties

sin (b) = \frac{5 sin ( 9 7 ^{\circ} )}{7}

General solutions for

sin (b) = \frac{5 sin ( 9 7 ^{\circ} )}{7}

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

b = arcsin (\frac{5 sin ( 9 7 ^{\circ} )}{7}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{5 sin ( 9 7 ^{\circ} )}{7}) + 36 0^{\circ} n

b = arcsin (\frac{5 sin ( 9 7 ^{\circ} )}{7}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{5 sin ( 9 7 ^{\circ} )}{7}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.78802 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.78802 \dots + 36 0^{\circ} n

tan (x) = \frac{5 + cos ( x )}{6 sin ( x ) cos ( x )}

cos (x - 1) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

cos (t) = \frac{21}{29}

cos (x) = sin (x - \frac{π}{3})

sin (x + \frac{π}{4}) + sin (x + \frac{π}{4}) = - 1

What is the general solution for (sin(97))/(14)=(sin(b))/(10) ?
The general solution for (sin(97))/(14)=(sin(b))/(10) is b=0.78802…+360n,b=180-0.78802…+360n