What is the general solution for 0.1*sin(θ)cos(53.13)+0.1*sin(θ)=0 ?

The general solution for 0.1*sin(θ)cos(53.13)+0.1*sin(θ)=0 is θ=360n,θ=180+360n

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0.1sin(θ)cos(53.13)+0.1sin(θ)=0

0.1 \cdot sin (θ) cos (53.1 3^{\circ}) + 0.1 \cdot sin (θ) = 0

θ = 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Radians

θ = 0 + 2 πn, θ = π + 2 πn

Solution steps

0.1 sin (θ) cos (53.1 3^{\circ}) + 0.1 sin (θ) = 0

Simplify

0.1 sin (θ) cos (53.1 3^{\circ}) + 0.1 sin (θ) : 0.16000 \dots sin (θ)

0.1 sin (θ) cos (53.1 3^{\circ}) + 0.1 sin (θ)

0.1 sin (θ) cos (53.1 3^{\circ}) = 0.06000 \dots sin (θ)

0.1 sin (θ) cos (53.1 3^{\circ})

53.1 3^{\circ} = 0.92729 \dots

53.1 3^{\circ}

Multiply the numbers:

1771 \cdot 3.14159 \dots = 5563.76058 \dots

= \frac{5563.76058 \dots}{6000}

Divide the numbers:

\frac{5563.76058 \dots}{6000} = 0.92729 \dots

= 0.92729 \dots

= 0.1 cos (0.92729 \dots) sin (θ)

Simplify

cos (0.92729 \dots) : 0.60000 \dots

cos (0.92729 \dots)

cos (0.92729 \dots) = 0.60000 \dots

= 0.60000 \dots

= 0.1 \cdot 0.60000 \dots sin (θ)

Multiply the numbers:

0.1 \cdot 0.60000 \dots = 0.06000 \dots

= 0.06000 \dots sin (θ)

= 0.06000 \dots sin (θ) + 0.1 sin (θ)

Add similar elements:

0.06000 \dots sin (θ) + 0.1 sin (θ) = 0.16000 \dots sin (θ)

= 0.16000 \dots sin (θ)

0.16000 \dots sin (θ) = 0

Divide both sides by

0.16000 \dots

0.16000 \dots sin (θ) = 0

Divide both sides by

0.16000 \dots

\frac{0.16000 \dots sin ( θ )}{0.16000 \dots} = \frac{0}{0.16000 \dots}

Simplify

sin (θ) = 0

sin (θ) = 0

General solutions for

sin (θ) = 0

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = 0 + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

θ = 0 + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Solve

θ = 0 + 36 0^{\circ} n : θ = 36 0^{\circ} n

θ = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

θ = 36 0^{\circ} n

θ = 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

tan (θ) = (1)

sec^{2} (x) = \frac{3 3}{π}

sin (θ) (sin (θ) + 1) = 0

6 tan^{2} (x) + 13 tan (x) + 6 = 0

0 = arctan (x) + \frac{π}{2}

What is the general solution for 0.1*sin(θ)cos(53.13)+0.1*sin(θ)=0 ?
The general solution for 0.1*sin(θ)cos(53.13)+0.1*sin(θ)=0 is θ=360n,θ=180+360n