What is the general solution for 0.75=sin(x) ?

The general solution for 0.75=sin(x) is x=0.84806…+2pin,x=pi-0.84806…+2pin

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0.75=sin(x)

0.75 = sin (x)

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Solution steps

0.75 = sin (x)

Switch sides

sin (x) = 0.75

Apply trig inverse properties

x = arcsin (0.75) + 2 πn, x = π - arcsin (0.75) + 2 πn

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

7 cos^{2} (x) - 1 = 5 cos (x), 0 \leq x \leq 2 π

2 cos^{2} (θ) = 3 sin (θ) + 3

cos (π x^{2}) = 0

sin^{2} (θ) + sin (θ) = 0, 0 \leq θ < 2 π

16 tan^{2} (θ) - 1 = 0

What is the general solution for 0.75=sin(x) ?
The general solution for 0.75=sin(x) is x=0.84806…+2pin,x=pi-0.84806…+2pin