What is the general solution for sin(x)= 9/10 ?

The general solution for sin(x)= 9/10 is x=1.11976…+2pin,x=pi-1.11976…+2pin

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sin(x)= 9/10

sin (x) = \frac{9}{10}

x = 1.11976 \dots + 2 πn, x = π - 1.11976 \dots + 2 πn

Degrees

x = 64.15806 \dots^{\circ} + 36 0^{\circ} n, x = 115.84193 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{9}{10}

Apply trig inverse properties

sin (x) = \frac{9}{10}

General solutions for

sin (x) = \frac{9}{10}

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

x = arcsin (\frac{9}{10}) + 2 πn, x = π - arcsin (\frac{9}{10}) + 2 πn

x = arcsin (\frac{9}{10}) + 2 πn, x = π - arcsin (\frac{9}{10}) + 2 πn

Show solutions in decimal form

x = 1.11976 \dots + 2 πn, x = π - 1.11976 \dots + 2 πn

4 sin (x) - sec (x) = 0

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

cos (x) = - \frac{1}{2}, 0 < x < 2 π

cot (θ) = cos (θ)

3 sin^{2} (θ) - cos (θ) + 1 = 0

What is the general solution for sin(x)= 9/10 ?
The general solution for sin(x)= 9/10 is x=1.11976…+2pin,x=pi-1.11976…+2pin