What is the general solution for sin(3v)=sin(18) ?

The general solution for sin(3v)=sin(18) is v=(0.31415…)/3+(360n)/3 ,v=60-(0.31415…)/3+(360n)/3

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sin(3v)=sin(18)

sin (3 v) = sin (1 8^{\circ})

v = \frac{0.31415 \dots}{3} + \frac{36 0 ^{\circ} n}{3}, v = 6 0^{\circ} - \frac{0.31415 \dots}{3} + \frac{36 0 ^{\circ} n}{3}

Solution steps

sin (3 v) = sin (1 8^{\circ})

sin (1 8^{\circ}) = \frac{2 3 - 5}{4}

sin (3 v) = \frac{2 3 - 5}{4}

Apply trig inverse properties

3 v = arcsin (\frac{2 3 - 5}{4}) + 36 0^{\circ} n, 3 v = 18 0^{\circ} - arcsin (\frac{2 3 - 5}{4}) + 36 0^{\circ} n

Solve

3 v = arcsin (\frac{2 3 - 5}{4}) + 36 0^{\circ} n : v = \frac{arcsin ( \frac{2 3 - 5}{4} )}{3} + \frac{36 0 ^{\circ} n}{3}

Solve

3 v = 18 0^{\circ} - arcsin (\frac{2 3 - 5}{4}) + 36 0^{\circ} n : v = 6 0^{\circ} - \frac{arcsin ( \frac{2 3 - 5}{4} )}{3} + \frac{36 0 ^{\circ} n}{3}

v = \frac{arcsin ( \frac{2 3 - 5}{4} )}{3} + \frac{36 0 ^{\circ} n}{3}, v = 6 0^{\circ} - \frac{arcsin ( \frac{2 3 - 5}{4} )}{3} + \frac{36 0 ^{\circ} n}{3}

Show solutions in decimal form

v = \frac{0.31415 \dots}{3} + \frac{36 0 ^{\circ} n}{3}, v = 6 0^{\circ} - \frac{0.31415 \dots}{3} + \frac{36 0 ^{\circ} n}{3}

tan (x) \cdot sin (x) - 3 sin (x) = 0

sin (θ) = \frac{( - \frac{2}{7} )}{2}

22 cos (θ) - 2 = 0

tan (x) = \frac{22}{326}

3 cos (6 x) = 2

What is the general solution for sin(3v)=sin(18) ?
The general solution for sin(3v)=sin(18) is v=(0.31415…)/3+(360n)/3 ,v=60-(0.31415…)/3+(360n)/3