What is the general solution for 6sin(2x-30)+2=0 ?

The general solution for 6sin(2x-30)+2=0 is x=180n+15-(0.33983…)/2 ,x=180n+90+15+(0.33983…)/2

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6sin(2x-30)+2=0

6 sin (2 x - 3 0^{\circ}) + 2 = 0

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{0.33983 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{0.33983 \dots}{2}

Solution steps

6 sin (2 x - 3 0^{\circ}) + 2 = 0

Move

2

to the right side

6 sin (2 x - 3 0^{\circ}) = - 2

Divide both sides by

6

sin (2 x - 3 0^{\circ}) = - \frac{1}{3}

Apply trig inverse properties

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n

Solve

2 x - 3 0^{\circ} = arcsin (- \frac{1}{3}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}

Solve

2 x - 3 0^{\circ} = 18 0^{\circ} + arcsin (\frac{1}{3}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{arcsin ( \frac{1}{3} )}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{arcsin ( \frac{1}{3} )}{2}

Show solutions in decimal form

x = 18 0^{\circ} n + 1 5^{\circ} - \frac{0.33983 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ} + \frac{0.33983 \dots}{2}

sin (x) = sin (\frac{π}{10})

\frac{1}{2} = sin (x)

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

x, 0.05 cos (x) = - sin (x)

cos (x^{\circ}) = \frac{20.26}{26.4473}

What is the general solution for 6sin(2x-30)+2=0 ?
The general solution for 6sin(2x-30)+2=0 is x=180n+15-(0.33983…)/2 ,x=180n+90+15+(0.33983…)/2