What is the general solution for 3sin(2x)=-1.76 ?

The general solution for 3sin(2x)=-1.76 is x=-(0.62693…)/2+pin,x= pi/2+(0.62693…)/2+pin

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Popular >

3sin(2x)=-1.76

Solution

3 sin (2 x) = - 1.76

Solution

x = - \frac{0.62693 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.62693 \dots}{2} + πn

Degrees

x = - 17.96040 \dots^{\circ} + 18 0^{\circ} n, x = 107.96040 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 sin (2 x) = - 1.76

Divide both sides by

3

3 sin (2 x) = - 1.76

Divide both sides by

3

\frac{3 sin ( 2 x )}{3} = \frac{- 1.76}{3}

Simplify

\frac{3 sin ( 2 x )}{3} = \frac{- 1.76}{3}

Simplify

\frac{3 sin ( 2 x )}{3} : sin (2 x)

\frac{3 sin ( 2 x )}{3}

Divide the numbers:

\frac{3}{3} = 1

= sin (2 x)

Simplify

\frac{- 1.76}{3} : - 0.58666 \dots

\frac{- 1.76}{3}

Apply the fraction rule:

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

= - \frac{1.76}{3}

Divide the numbers:

\frac{1.76}{3} = 0.58666 \dots

= - 0.58666 \dots

sin (2 x) = - 0.58666 \dots

sin (2 x) = - 0.58666 \dots

sin (2 x) = - 0.58666 \dots

Apply trig inverse properties

sin (2 x) = - 0.58666 \dots

General solutions for

sin (2 x) = - 0.58666 \dots

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

2 x = arcsin (- 0.58666 \dots) + 2 πn, 2 x = π + arcsin (0.58666 \dots) + 2 πn

2 x = arcsin (- 0.58666 \dots) + 2 πn, 2 x = π + arcsin (0.58666 \dots) + 2 πn

Solve

2 x = arcsin (- 0.58666 \dots) + 2 πn : x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn

2 x = arcsin (- 0.58666 \dots) + 2 πn

Simplify

arcsin (- 0.58666 \dots) + 2 πn : - arcsin (0.58666 \dots) + 2 πn

arcsin (- 0.58666 \dots) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- 0.58666 \dots) = - arcsin (0.58666 \dots)

= - arcsin (0.58666 \dots) + 2 πn

2 x = - arcsin (0.58666 \dots) + 2 πn

Divide both sides by

2

2 x = - arcsin (0.58666 \dots) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arcsin ( 0.58666 \dots )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn

x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn

Solve

2 x = π + arcsin (0.58666 \dots) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

2 x = π + arcsin (0.58666 \dots) + 2 πn

Divide both sides by

2

2 x = π + arcsin (0.58666 \dots) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

x = - \frac{arcsin ( 0.58666 \dots )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( 0.58666 \dots )}{2} + πn

Show solutions in decimal form

x = - \frac{0.62693 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.62693 \dots}{2} + πn

Popular Examples

sin(θ)= 5/12

sin (θ) = \frac{5}{12}

sin(2θ)=(-1)/2

sin (2 θ) = \frac{- 1}{2}

tan(θ)=(-68.1)/(10)

tan (θ) = \frac{- 68.1}{10}

cos(2θ)+6sin^2(θ)=4,0<= x<2pi

cos (2 θ) + 6 sin^{2} (θ) = 4, 0 \leq x < 2 π

sin(a)= 24/25

sin (a) = \frac{24}{25}

Frequently Asked Questions (FAQ)

What is the general solution for 3sin(2x)=-1.76 ?
The general solution for 3sin(2x)=-1.76 is x=-(0.62693…)/2+pin,x= pi/2+(0.62693…)/2+pin