What is the general solution for sin(t)= 2/5 ?

The general solution for sin(t)= 2/5 is t=0.41151…+2pin,t=pi-0.41151…+2pin

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sin(t)= 2/5

sin (t) = \frac{2}{5}

t = 0.41151 \dots + 2 πn, t = π - 0.41151 \dots + 2 πn

Solution steps

sin (t) = \frac{2}{5}

Apply trig inverse properties

t = arcsin (\frac{2}{5}) + 2 πn, t = π - arcsin (\frac{2}{5}) + 2 πn

Show solutions in decimal form

t = 0.41151 \dots + 2 πn, t = π - 0.41151 \dots + 2 πn

tan (x) - 1 = sec (x)

0 = sec (x)

tan (2 x) = - 2

tan^{3} (x) - 1 tan (x) = 0

2 cos (x) - 1 = 0, 0 \leq x \leq 2 π

What is the general solution for sin(t)= 2/5 ?
The general solution for sin(t)= 2/5 is t=0.41151…+2pin,t=pi-0.41151…+2pin