What is the general solution for sin(4θ)=0.345 ?

The general solution for sin(4θ)=0.345 is θ=(0.35223…)/4+(pin)/2 ,θ= pi/4-(0.35223…)/4+(pin)/2

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sin(4θ)=0.345

sin (4 θ) = 0.345

θ = \frac{0.35223 \dots}{4} + \frac{πn}{2}, θ = \frac{π}{4} - \frac{0.35223 \dots}{4} + \frac{πn}{2}

Degrees

θ = 5.04544 \dots^{\circ} + 9 0^{\circ} n, θ = 39.95455 \dots^{\circ} + 9 0^{\circ} n

Solution steps

sin (4 θ) = 0.345

Apply trig inverse properties

sin (4 θ) = 0.345

General solutions for

sin (4 θ) = 0.345

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

4 θ = arcsin (0.345) + 2 πn, 4 θ = π - arcsin (0.345) + 2 πn

4 θ = arcsin (0.345) + 2 πn, 4 θ = π - arcsin (0.345) + 2 πn

Solve

4 θ = arcsin (0.345) + 2 πn : θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

4 θ = arcsin (0.345) + 2 πn

Divide both sides by

4

4 θ = arcsin (0.345) + 2 πn

Divide both sides by

4

\frac{4 θ}{4} = \frac{arcsin ( 0.345 )}{4} + \frac{2 πn}{4}

Simplify

θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

Solve

4 θ = π - arcsin (0.345) + 2 πn : θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

4 θ = π - arcsin (0.345) + 2 πn

Divide both sides by

4

4 θ = π - arcsin (0.345) + 2 πn

Divide both sides by

4

\frac{4 θ}{4} = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{2 πn}{4}

Simplify

θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}, θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{0.35223 \dots}{4} + \frac{πn}{2}, θ = \frac{π}{4} - \frac{0.35223 \dots}{4} + \frac{πn}{2}

- 3 = cot^{2} (x) + 3 csc (x)

4 cos^{2} (θ) + 3 cos (θ) = 1

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

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

400 = 812.25 + 400 - 1140 cos (a)

What is the general solution for sin(4θ)=0.345 ?
The general solution for sin(4θ)=0.345 is θ=(0.35223…)/4+(pin)/2 ,θ= pi/4-(0.35223…)/4+(pin)/2