What is the general solution for 4sin(θ)+3=5 ?

The general solution for 4sin(θ)+3=5 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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4sin(θ)+3=5

4 sin (θ) + 3 = 5

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (θ) + 3 = 5

Move

3

to the right side

4 sin (θ) + 3 = 5

Subtract

3

from both sides

4 sin (θ) + 3 - 3 = 5 - 3

Simplify

4 sin (θ) = 2

4 sin (θ) = 2

Divide both sides by

4

4 sin (θ) = 2

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{2}{4}

Simplify

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

General solutions for

sin (θ) = \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

5 sin (x) cos (x) = 7 cos (x)

tan (\frac{θ}{2}) - sin (θ) = 0

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

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{2}{2}

sec^{2} (x) - 2 tan (x) = 4

What is the general solution for 4sin(θ)+3=5 ?
The general solution for 4sin(θ)+3=5 is θ= pi/6+2pin,θ=(5pi)/6+2pin