What is the general solution for 2.5=10sin(x) ?

The general solution for 2.5=10sin(x) is x=0.25268…+2pin,x=pi-0.25268…+2pin

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2.5=10sin(x)

2.5 = 10 sin (x)

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Degrees

x = 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 165.52248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2.5 = 10 sin (x)

Switch sides

10 sin (x) = 2.5

Divide both sides by

10

10 sin (x) = 2.5

Divide both sides by

10

\frac{10 sin ( x )}{10} = \frac{2.5}{10}

Simplify

sin (x) = 0.25

sin (x) = 0.25

Apply trig inverse properties

sin (x) = 0.25

General solutions for

sin (x) = 0.25

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

x = arcsin (0.25) + 2 πn, x = π - arcsin (0.25) + 2 πn

x = arcsin (0.25) + 2 πn, x = π - arcsin (0.25) + 2 πn

Show solutions in decimal form

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

4.797896 cos (0.568 x - 2.595) = 0

2 cos (x) - 1 = 2 cos (2 x)

5 sec (x) - 2 = 3 cos (x)

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

tan (x) = \frac{20}{30}

What is the general solution for 2.5=10sin(x) ?
The general solution for 2.5=10sin(x) is x=0.25268…+2pin,x=pi-0.25268…+2pin