What is the general solution for 3sin(x)+2=1.5 ?

The general solution for 3sin(x)+2=1.5 is x=-0.16744…+2pin,x=pi+0.16744…+2pin

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3sin(x)+2=1.5

3 sin (x) + 2 = 1.5

x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

Degrees

x = - 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 189.59406 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 sin (x) + 2 = 1.5

Move

2

to the right side

3 sin (x) + 2 = 1.5

Subtract

2

from both sides

3 sin (x) + 2 - 2 = 1.5 - 2

Simplify

3 sin (x) = - 0.5

3 sin (x) = - 0.5

Divide both sides by

3

3 sin (x) = - 0.5

Divide both sides by

3

\frac{3 sin ( x )}{3} = \frac{- 0.5}{3}

Simplify

\frac{3 sin ( x )}{3} = \frac{- 0.5}{3}

Simplify

\frac{3 sin ( x )}{3} : sin (x)

\frac{3 sin ( x )}{3}

Divide the numbers:

\frac{3}{3} = 1

= sin (x)

Simplify

\frac{- 0.5}{3} : - 0.16666 \dots

\frac{- 0.5}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{0.5}{3}

Divide the numbers:

\frac{0.5}{3} = 0.16666 \dots

= - 0.16666 \dots

sin (x) = - 0.16666 \dots

sin (x) = - 0.16666 \dots

sin (x) = - 0.16666 \dots

Apply trig inverse properties

sin (x) = - 0.16666 \dots

General solutions for

sin (x) = - 0.16666 \dots

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

x = arcsin (- 0.16666 \dots) + 2 πn, x = π + arcsin (0.16666 \dots) + 2 πn

x = arcsin (- 0.16666 \dots) + 2 πn, x = π + arcsin (0.16666 \dots) + 2 πn

Show solutions in decimal form

x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

3 sec^{2} (x) - 2 tan (x) - 4 = 0

9 sin^{2} (x) - 1 = 0

sin (x) = \frac{1}{3.5}

tan (θ) = 5, 96

1 = 1 - cos (θ)

What is the general solution for 3sin(x)+2=1.5 ?
The general solution for 3sin(x)+2=1.5 is x=-0.16744…+2pin,x=pi+0.16744…+2pin