What is the general solution for (35)/(sin(90))=(27)/(sin(y)) ?

The general solution for (35)/(sin(90))=(27)/(sin(y)) is y=0.88108…+360n,y=180-0.88108…+360n

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(35)/(sin(90))=(27)/(sin(y))

\frac{35}{sin ( 9 0 ^{\circ} )} = \frac{27}{sin ( y )}

y = 0.88108 \dots + 36 0^{\circ} n, y = 18 0^{\circ} - 0.88108 \dots + 36 0^{\circ} n

Solution steps

\frac{35}{sin ( 9 0 ^{\circ} )} = \frac{27}{sin ( y )}

sin (9 0^{\circ}) = 1

\frac{35}{1} = \frac{27}{sin ( y )}

Cross multiply

35 sin (y) = 27

Divide both sides by

35

sin (y) = \frac{27}{35}

Verify Solutions

Find undefined (singularity) points:

sin (y) = 0

Combine undefined points with solutions:

sin (y) = \frac{27}{35}

Apply trig inverse properties

y = arcsin (\frac{27}{35}) + 36 0^{\circ} n, y = 18 0^{\circ} - arcsin (\frac{27}{35}) + 36 0^{\circ} n

Show solutions in decimal form

y = 0.88108 \dots + 36 0^{\circ} n, y = 18 0^{\circ} - 0.88108 \dots + 36 0^{\circ} n

4 cos^{2} (x) + 2 cos (x) - 22 cos (x) = 2

sin (x + 2 0^{\circ}) \cdot csc (7 0^{\circ}) = 1

\frac{π}{2} = \frac{arcsin ( x )}{c}

6 sin^{2} (x) + 16 sin (x) cos (x) - 6 cos^{2} (x) = 0

sec^{2} (t) = 0

What is the general solution for (35)/(sin(90))=(27)/(sin(y)) ?
The general solution for (35)/(sin(90))=(27)/(sin(y)) is y=0.88108…+360n,y=180-0.88108…+360n