What is the general solution for sin(x)-0.75=0 ?

The general solution for sin(x)-0.75=0 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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sin(x)-0.75=0

sin (x) - 0.75 = 0

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

Degrees

x = 48.59037 \dots^{\circ} + 36 0^{\circ} n, x = 131.40962 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) - 0.75 = 0

Move

0.75

to the right side

sin (x) - 0.75 = 0

Add

0.75

to both sides

sin (x) - 0.75 + 0.75 = 0 + 0.75

Simplify

sin (x) = 0.75

sin (x) = 0.75

Apply trig inverse properties

sin (x) = 0.75

General solutions for

sin (x) = 0.75

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

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

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

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

sin (x) = sin (x + 1)

1 + cos (2 x) = sin (2 x)

cos (a) = \frac{6}{7.5}

4 - 4 cos (2 x) = 5 - 4 cos (x)

What is the general solution for sin(x)-0.75=0 ?
The general solution for sin(x)-0.75=0 is x=0.84806…+2pin,x=pi-0.84806…+2pin