What is the general solution for sin(x)=(4.1)/(7.1) ?

The general solution for sin(x)=(4.1)/(7.1) is x=0.61561…+2pin,x=pi-0.61561…+2pin

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sin(x)=(4.1)/(7.1)

sin (x) = \frac{4.1}{7.1}

x = 0.61561 \dots + 2 πn, x = π - 0.61561 \dots + 2 πn

Degrees

x = 35.27242 \dots^{\circ} + 36 0^{\circ} n, x = 144.72757 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{4.1}{7.1}

Apply trig inverse properties

sin (x) = \frac{4.1}{7.1}

General solutions for

sin (x) = \frac{4.1}{7.1}

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

x = arcsin (\frac{4.1}{7.1}) + 2 πn, x = π - arcsin (\frac{4.1}{7.1}) + 2 πn

x = arcsin (\frac{4.1}{7.1}) + 2 πn, x = π - arcsin (\frac{4.1}{7.1}) + 2 πn

Show solutions in decimal form

x = 0.61561 \dots + 2 πn, x = π - 0.61561 \dots + 2 πn

(1 + cos^{2} (a)) sin^{2} (a) = 1

cos^{4} (x) = cos^{23} (x)

cos^{4} (x) + 2 cos^{2} (x) = 1

cos^{2} (x) + sin^{2} (x) = cos^{5} (x)

sin (x - 4 5^{5}) = \frac{( 2 )}{2}

What is the general solution for sin(x)=(4.1)/(7.1) ?
The general solution for sin(x)=(4.1)/(7.1) is x=0.61561…+2pin,x=pi-0.61561…+2pin