What is the general solution for sin(x)= 9/12 ?

The general solution for sin(x)= 9/12 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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sin(x)= 9/12

sin (x) = \frac{9}{12}

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Degrees

x = 48.59037 \dots^{\circ} + 36 0^{\circ} n, x = 131.40962 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{9}{12}

Cancel the common factor:

3

sin (x) = \frac{3}{4}

Apply trig inverse properties

sin (x) = \frac{3}{4}

General solutions for

sin (x) = \frac{3}{4}

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

x = arcsin (\frac{3}{4}) + 2 πn, x = π - arcsin (\frac{3}{4}) + 2 πn

x = arcsin (\frac{3}{4}) + 2 πn, x = π - arcsin (\frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

- 2 cos (x) + 3 sin (x) = 2

cos (x + \frac{π}{6}) - 1 = cos (x - \frac{π}{6})

cos (2 x) cos (x) - sin (2 x) sin (x) = \frac{- 3}{2}

2 sin (θ) = cos (2 θ)

tan (θ) = \frac{4}{- 4}

What is the general solution for sin(x)= 9/12 ?
The general solution for sin(x)= 9/12 is x=0.84806…+2pin,x=pi-0.84806…+2pin