What is the general solution for 3sqrt(2)sin(θ)-3=0 ?

The general solution for 3sqrt(2)sin(θ)-3=0 is θ= pi/4+2pin,θ=(3pi)/4+2pin

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3sqrt(2)sin(θ)-3=0

32 sin (θ) - 3 = 0

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

Degrees

θ = 4 5^{\circ} + 36 0^{\circ} n, θ = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

32 sin (θ) - 3 = 0

Move

3

to the right side

32 sin (θ) - 3 = 0

Add

3

to both sides

32 sin (θ) - 3 + 3 = 0 + 3

Simplify

32 sin (θ) = 3

32 sin (θ) = 3

Divide both sides by

32

32 sin (θ) = 3

Divide both sides by

32

\frac{3 2 sin ( θ )}{3 2} = \frac{3}{3 2}

Simplify

\frac{3 2 sin ( θ )}{3 2} = \frac{3}{3 2}

Simplify

\frac{3 2 sin ( θ )}{3 2} : sin (θ)

\frac{3 2 sin ( θ )}{3 2}

Divide the numbers:

\frac{3}{3} = 1

= \frac{2 sin ( θ )}{2}

Cancel the common factor:

2

= sin (θ)

Simplify

\frac{3}{3 2} : \frac{2}{2}

\frac{3}{3 2}

Divide the numbers:

\frac{3}{3} = 1

= \frac{1}{2}

Rationalize

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{2}{2}

= \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

General solutions for

sin (θ) = \frac{2}{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}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

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

(2 sin (x) - 1) (2 cos^{2} (x) - 1) = 0

6 sec^{2} (x) - 8 = tan (x)

cos (θ) a = \frac{π}{4}

cos (x) = \frac{59}{95}

What is the general solution for 3sqrt(2)sin(θ)-3=0 ?
The general solution for 3sqrt(2)sin(θ)-3=0 is θ= pi/4+2pin,θ=(3pi)/4+2pin