What is the general solution for (sin(1.3785)}{70}=\frac{sin(a))/7 ?

The general solution for (sin(1.3785)}{70}=\frac{sin(a))/7 is a=0.09831…+2pin,a=pi-0.09831…+2pin

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(sin(1.3785)}{70}=\frac{sin(a))/7

\frac{sin ( 1.3785 )}{70} = \frac{sin ( a )}{7}

a = 0.09831 \dots + 2 πn, a = π - 0.09831 \dots + 2 πn

Degrees

a = 5.63304 \dots^{\circ} + 36 0^{\circ} n, a = 174.36695 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{sin ( 1.3785 )}{70} = \frac{sin ( a )}{7}

sin (1.3785) = sin (\frac{2757}{2000})

sin (1.3785)

\frac{sin ( \frac{2757}{2000} )}{70} = \frac{sin ( a )}{7}

Switch sides

\frac{sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{70}

Multiply both sides by

10

\frac{sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{70}

Multiply both sides by

10

\frac{sin ( a )}{7} \cdot 10 = \frac{sin ( \frac{2757}{2000} )}{70} \cdot 10

Simplify

\frac{sin ( a )}{7} \cdot 10 = \frac{sin ( \frac{2757}{2000} )}{70} \cdot 10

Simplify

\frac{sin ( a )}{7} \cdot 10 : \frac{10 sin ( a )}{7}

\frac{sin ( a )}{7} \cdot 10

Multiply fractions:

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

= \frac{sin ( a ) \cdot 10}{7}

Simplify

\frac{sin ( \frac{2757}{2000} )}{70} \cdot 10 : \frac{sin ( \frac{2757}{2000} )}{7}

\frac{sin ( \frac{2757}{2000} )}{70} \cdot 10

Multiply fractions:

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

= \frac{sin ( \frac{2757}{2000} ) \cdot 10}{70}

Cancel the common factor:

10

= \frac{sin ( \frac{2757}{2000} )}{7}

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

Multiply both sides by

7

\frac{10 sin ( a )}{7} = \frac{sin ( \frac{2757}{2000} )}{7}

Multiply both sides by

7

\frac{7 \cdot 10 sin ( a )}{7} = \frac{7 sin ( \frac{2757}{2000} )}{7}

Simplify

10 sin (a) = sin (\frac{2757}{2000})

10 sin (a) = sin (\frac{2757}{2000})

Divide both sides by

10

10 sin (a) = sin (\frac{2757}{2000})

Divide both sides by

10

\frac{10 sin ( a )}{10} = \frac{sin ( \frac{2757}{2000} )}{10}

Simplify

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

Apply trig inverse properties

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

General solutions for

sin (a) = \frac{sin ( \frac{2757}{2000} )}{10}

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

a = arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn, a = π - arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn

a = arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn, a = π - arcsin (\frac{sin ( \frac{2757}{2000} )}{10}) + 2 πn

Show solutions in decimal form

a = 0.09831 \dots + 2 πn, a = π - 0.09831 \dots + 2 πn

cos^{2} (x) - 6 cos (x) - 7 = 0

cos (θ) = 0, 0 \leq θ \leq 2 π

- 2 sin (x) - 2 + 4 sin^{2} (x) = 0

cos (x) = - \frac{3}{5}, π < x < \frac{3 π}{2}, sin (\frac{x}{2})

3 0^{\circ} = arccos (\frac{6}{x ( 3 )})

What is the general solution for (sin(1.3785)}{70}=\frac{sin(a))/7 ?
The general solution for (sin(1.3785)}{70}=\frac{sin(a))/7 is a=0.09831…+2pin,a=pi-0.09831…+2pin