What is the general solution for (25)/(sin(x))=(18)/(sin(36)) ?

The general solution for (25)/(sin(x))=(18)/(sin(36)) is x=0.95509…+360n,x=180-0.95509…+360n

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(25)/(sin(x))=(18)/(sin(36))

\frac{25}{sin ( x )} = \frac{18}{sin ( 3 6 ^{\circ} )}

x = 0.95509 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.95509 \dots + 36 0^{\circ} n

Solution steps

\frac{25}{sin ( x )} = \frac{18}{sin ( 3 6 ^{\circ} )}

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

\frac{25}{sin ( x )} = \frac{18}{\frac{2 5 - 5}{4}}

Cross multiply

\frac{25 2 5 - 5}{4} = sin (x) \cdot 18

Switch sides

sin (x) \cdot 18 = \frac{25 2 5 - 5}{4}

Divide both sides by

18

sin (x) = \frac{25 2 5 - 5}{72}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{25 2 5 - 5}{72}

Apply trig inverse properties

x = arcsin (\frac{25 2 5 - 5}{72}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{25 2 5 - 5}{72}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.95509 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.95509 \dots + 36 0^{\circ} n

7 tan (3 x) - 21 tan (x) = 0

cos (A) = - \frac{3}{25}

tan (a) = \frac{12}{5}

cos (θ) + 2 tan (θ) = sec (θ)

\frac{9 tan ( θ )}{10 - tan ^{2} ( θ )} = 1

What is the general solution for (25)/(sin(x))=(18)/(sin(36)) ?
The general solution for (25)/(sin(x))=(18)/(sin(36)) is x=0.95509…+360n,x=180-0.95509…+360n