What is the general solution for 6sin(C)+sqrt(8)=0 ?

The general solution for 6sin(C)+sqrt(8)=0 is C=-0.49088…+2pin,C=pi+0.49088…+2pin

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6sin(C)+sqrt(8)=0

6 sin (C) + 8 = 0

C = - 0.49088 \dots + 2 πn, C = π + 0.49088 \dots + 2 πn

Solution steps

6 sin (C) + 8 = 0

Simplify

6 sin (C) + 8 : 6 sin (C) + 22

6 sin (C) + 22 = 0

Move

22

to the right side

6 sin (C) = - 22

Divide both sides by

6

sin (C) = - \frac{2}{3}

Apply trig inverse properties

C = arcsin (- \frac{2}{3}) + 2 πn, C = π + arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

C = - 0.49088 \dots + 2 πn, C = π + 0.49088 \dots + 2 πn

cos (2 t) = - sin (t)

sin^{2} (x) - 5 cos (x) - 5 = 0

\frac{1 + tan ^{2} ( 27 \cdot θ )}{1 - tan ^{2} ( 27 \cdot θ )} = 2

tan (x) = - cot (x)

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

What is the general solution for 6sin(C)+sqrt(8)=0 ?
The general solution for 6sin(C)+sqrt(8)=0 is C=-0.49088…+2pin,C=pi+0.49088…+2pin