What is the general solution for sin(x)= 10/12 ?

The general solution for sin(x)= 10/12 is x=0.98511…+2pin,x=pi-0.98511…+2pin

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sin(x)= 10/12

sin (x) = \frac{10}{12}

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

Solution steps

sin (x) = \frac{10}{12}

Cancel the common factor:

2

sin (x) = \frac{5}{6}

Apply trig inverse properties

x = arcsin (\frac{5}{6}) + 2 πn, x = π - arcsin (\frac{5}{6}) + 2 πn

Show solutions in decimal form

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn

3 cot (x) = - 1, 0 \leq x \leq 2 π

sin (x) = \frac{10}{14}

cos (x) = \frac{9}{15}

8 sin^{2} (x) + 12 sin (x) + 4 = 0

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

What is the general solution for sin(x)= 10/12 ?
The general solution for sin(x)= 10/12 is x=0.98511…+2pin,x=pi-0.98511…+2pin