What is the general solution for sin(x)=-(sqrt(7))/4 ?

The general solution for sin(x)=-(sqrt(7))/4 is x=-0.72273…+2pin,x=pi+0.72273…+2pin

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sin(x)=-(sqrt(7))/4

sin (x) = - \frac{7}{4}

x = - 0.72273 \dots + 2 πn, x = π + 0.72273 \dots + 2 πn

Solution steps

sin (x) = - \frac{7}{4}

Apply trig inverse properties

x = arcsin (- \frac{7}{4}) + 2 πn, x = π + arcsin (\frac{7}{4}) + 2 πn

Show solutions in decimal form

x = - 0.72273 \dots + 2 πn, x = π + 0.72273 \dots + 2 πn

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

sin (x) + 2 = tan (x)

- 2 sin (\frac{θ}{2}) = 0

cos^{3} (θ) + cos^{2} (θ) - cos (θ) - 1 = 0

2 sin^{2} (x) - 2 sin (x) = 0

What is the general solution for sin(x)=-(sqrt(7))/4 ?
The general solution for sin(x)=-(sqrt(7))/4 is x=-0.72273…+2pin,x=pi+0.72273…+2pin