What is the general solution for sin(x)=(sin(45))/(1.3) ?

The general solution for sin(x)=(sin(45))/(1.3) is x=0.57511…+360n,x=180-0.57511…+360n

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sin(x)=(sin(45))/(1.3)

sin (x) = \frac{sin ( 4 5 ^{\circ} )}{1.3}

x = 0.57511 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.57511 \dots + 36 0^{\circ} n

Radians

x = 0.57511 \dots + 2 πn, x = π - 0.57511 \dots + 2 πn

Solution steps

sin (x) = \frac{sin ( 4 5 ^{\circ} )}{1.3}

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

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}

= \frac{2}{2}

= \frac{2}{2}

sin (x) = \frac{\frac{2}{2}}{1.3}

Simplify

\frac{\frac{2}{2}}{1.3} : \frac{2}{2.6}

\frac{\frac{2}{2}}{1.3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{2}{2 \cdot 1.3}

Multiply the numbers:

2 \cdot 1.3 = 2.6

= \frac{2}{2.6}

Apply trig inverse properties

sin (x) = \frac{2}{2.6}

General solutions for

sin (x) = \frac{2}{2.6}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{2}{2.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{2.6}) + 36 0^{\circ} n

x = arcsin (\frac{2}{2.6}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{2.6}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.57511 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.57511 \dots + 36 0^{\circ} n

arctan (x) + arctan (1 - x) = arctan (\frac{9}{7})

(2 cos (x) + 1) (sin (x) - 1) = 0

3 cos^{2} (θ) - sin^{2} (θ) = 0

x, cos^{2} (x y) = \frac{1}{4}

sin (x) = (\frac{6}{4})

What is the general solution for sin(x)=(sin(45))/(1.3) ?
The general solution for sin(x)=(sin(45))/(1.3) is x=0.57511…+360n,x=180-0.57511…+360n