What is the general solution for 8sin(θ)+5=0 ?

The general solution for 8sin(θ)+5=0 is θ=-0.67513…+2pin,θ=pi+0.67513…+2pin

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8sin(θ)+5=0

8 sin (θ) + 5 = 0

θ = - 0.67513 \dots + 2 πn, θ = π + 0.67513 \dots + 2 πn

Solution steps

8 sin (θ) + 5 = 0

Move

5

to the right side

8 sin (θ) = - 5

Divide both sides by

8

sin (θ) = - \frac{5}{8}

Apply trig inverse properties

θ = arcsin (- \frac{5}{8}) + 2 πn, θ = π + arcsin (\frac{5}{8}) + 2 πn

Show solutions in decimal form

θ = - 0.67513 \dots + 2 πn, θ = π + 0.67513 \dots + 2 πn

2 cos^{2} (x) + 3 cos (x) = - 1, 0 \leq x \leq 2 π

9 cos (2 θ) = - 9 cos (θ)

3 sec^{2} (x) - 3 sec (x) = 6

tan (2 θ) = - 3

sin (x) + cos (x) = \frac{2}{5}

What is the general solution for 8sin(θ)+5=0 ?
The general solution for 8sin(θ)+5=0 is θ=-0.67513…+2pin,θ=pi+0.67513…+2pin