What is the general solution for sin(y)=(50)/(65.3) ?

The general solution for sin(y)=(50)/(65.3) is y=0.87212…+2pin,y=pi-0.87212…+2pin

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sin(y)=(50)/(65.3)

sin (y) = \frac{50}{65.3}

y = 0.87212 \dots + 2 πn, y = π - 0.87212 \dots + 2 πn

Degrees

y = 49.96902 \dots^{\circ} + 36 0^{\circ} n, y = 130.03097 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (y) = \frac{50}{65.3}

Apply trig inverse properties

sin (y) = \frac{50}{65.3}

General solutions for

sin (y) = \frac{50}{65.3}

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

y = arcsin (\frac{50}{65.3}) + 2 πn, y = π - arcsin (\frac{50}{65.3}) + 2 πn

y = arcsin (\frac{50}{65.3}) + 2 πn, y = π - arcsin (\frac{50}{65.3}) + 2 πn

Show solutions in decimal form

y = 0.87212 \dots + 2 πn, y = π - 0.87212 \dots + 2 πn

0.26 = \frac{1 - sin ( x )}{1 + sin ( x )}

sec (x) = - 2, 0 \leq x \leq 2 π

2 tan^{2} (x) = 2

2 cos (t) = 1

cos (x) = \frac{2}{13}

What is the general solution for sin(y)=(50)/(65.3) ?
The general solution for sin(y)=(50)/(65.3) is y=0.87212…+2pin,y=pi-0.87212…+2pin