What is the general solution for sin(x)= 23/24 ?

The general solution for sin(x)= 23/24 is x=1.28110…+2pin,x=pi-1.28110…+2pin

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sin(x)= 23/24

sin (x) = \frac{23}{24}

x = 1.28110 \dots + 2 πn, x = π - 1.28110 \dots + 2 πn

Solution steps

sin (x) = \frac{23}{24}

Apply trig inverse properties

x = arcsin (\frac{23}{24}) + 2 πn, x = π - arcsin (\frac{23}{24}) + 2 πn

Show solutions in decimal form

x = 1.28110 \dots + 2 πn, x = π - 1.28110 \dots + 2 πn

5 - 5 cos (x) = 4 sin^{2} (x)

3 cot^{2} (x) - 14 csc (x) - 2 = 0

250 = 100 \cdot 5 \cdot cos (x)

cos (θ) = - \frac{2}{5}

tan (x) = \frac{1}{sin ( 2 x )}, 0 \leq x \leq π

What is the general solution for sin(x)= 23/24 ?
The general solution for sin(x)= 23/24 is x=1.28110…+2pin,x=pi-1.28110…+2pin