What is the general solution for sin(x)= 12/15 ?

The general solution for sin(x)= 12/15 is x=0.92729…+2pin,x=pi-0.92729…+2pin

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sin(x)= 12/15

sin (x) = \frac{12}{15}

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

Degrees

x = 53.13010 \dots^{\circ} + 36 0^{\circ} n, x = 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{12}{15}

Cancel the common factor:

3

sin (x) = \frac{4}{5}

Apply trig inverse properties

sin (x) = \frac{4}{5}

General solutions for

sin (x) = \frac{4}{5}

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

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

cos (2 x) - cos (4 x) = 0

tan (x) (cot (x) - 3) = 0

sin (5 x) + sin (7 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ}

- cos (θ) + 1 = 2 sin^{2} (θ)

arcsin (x) = \frac{3 π}{7}

What is the general solution for sin(x)= 12/15 ?
The general solution for sin(x)= 12/15 is x=0.92729…+2pin,x=pi-0.92729…+2pin