What is the general solution for 2sin(x)-1=0.5 ?

The general solution for 2sin(x)-1=0.5 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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2sin(x)-1=0.5

2 sin (x) - 1 = 0.5

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

2 sin (x) - 1 = 0.5

Move

1

to the right side

2 sin (x) - 1 = 0.5

Add

1

to both sides

2 sin (x) - 1 + 1 = 0.5 + 1

Simplify

2 sin (x) = 1.5

2 sin (x) = 1.5

Divide both sides by

2

2 sin (x) = 1.5

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{1.5}{2}

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 (x) - 1) (2 sin (x) + 1) = 0

sin (θ) = \frac{1}{2}, θ

tan (x) = \frac{40}{34}

cot (b) = - 5

sin^{2} (x) - cos^{3} (x) = 0

What is the general solution for 2sin(x)-1=0.5 ?
The general solution for 2sin(x)-1=0.5 is x=0.84806…+2pin,x=pi-0.84806…+2pin