What is the general solution for sin(x)=(sqrt(21))/5 ?

The general solution for sin(x)=(sqrt(21))/5 is x=1.15927…+2pin,x=pi-1.15927…+2pin

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sin(x)=(sqrt(21))/5

sin (x) = \frac{21}{5}

x = 1.15927 \dots + 2 πn, x = π - 1.15927 \dots + 2 πn

Degrees

x = 66.42182 \dots^{\circ} + 36 0^{\circ} n, x = 113.57817 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{21}{5}

Apply trig inverse properties

sin (x) = \frac{21}{5}

General solutions for

sin (x) = \frac{21}{5}

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

x = arcsin (\frac{21}{5}) + 2 πn, x = π - arcsin (\frac{21}{5}) + 2 πn

x = arcsin (\frac{21}{5}) + 2 πn, x = π - arcsin (\frac{21}{5}) + 2 πn

Show solutions in decimal form

x = 1.15927 \dots + 2 πn, x = π - 1.15927 \dots + 2 πn

tan (\frac{θ}{2} - \frac{π}{6}) = 1

1 + 2 sin (θ) = csc (θ)

- 6 = - 4 + sec (x + \frac{π}{4})

2 sin^{2} (x) + 3 sin (x) = 2

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

What is the general solution for sin(x)=(sqrt(21))/5 ?
The general solution for sin(x)=(sqrt(21))/5 is x=1.15927…+2pin,x=pi-1.15927…+2pin