What is the general solution for sin(30)=cos(2x) ?

The general solution for sin(30)=cos(2x) is x=30+180n,x=150+180n

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Popular >

sin(30)=cos(2x)

Solution

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

Solution

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

Radians

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Solution steps

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

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

\frac{1}{2} = cos (2 x)

Switch sides

cos (2 x) = \frac{1}{2}

General solutions for

cos (2 x) = \frac{1}{2}

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 x = 6 0^{\circ} + 36 0^{\circ} n, 2 x = 30 0^{\circ} + 36 0^{\circ} n

2 x = 6 0^{\circ} + 36 0^{\circ} n, 2 x = 30 0^{\circ} + 36 0^{\circ} n

Solve

2 x = 6 0^{\circ} + 36 0^{\circ} n : x = 3 0^{\circ} + 18 0^{\circ} n

2 x = 6 0^{\circ} + 36 0^{\circ} n

Divide both sides by

2

2 x = 6 0^{\circ} + 36 0^{\circ} n

Divide both sides by

2

\frac{2 x}{2} = \frac{6 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplify

\frac{2 x}{2} = \frac{6 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{6 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} : 3 0^{\circ} + 18 0^{\circ} n

\frac{6 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

\frac{6 0 ^{\circ}}{2} = 3 0^{\circ}

\frac{6 0 ^{\circ}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{18 0 ^{\circ}}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= 3 0^{\circ}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Divide the numbers:

\frac{2}{2} = 1

= 18 0^{\circ} n

= 3 0^{\circ} + 18 0^{\circ} n

x = 3 0^{\circ} + 18 0^{\circ} n

x = 3 0^{\circ} + 18 0^{\circ} n

x = 3 0^{\circ} + 18 0^{\circ} n

Solve

2 x = 30 0^{\circ} + 36 0^{\circ} n : x = 15 0^{\circ} + 18 0^{\circ} n

2 x = 30 0^{\circ} + 36 0^{\circ} n

Divide both sides by

2

2 x = 30 0^{\circ} + 36 0^{\circ} n

Divide both sides by

2

\frac{2 x}{2} = \frac{30 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplify

\frac{2 x}{2} = \frac{30 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{30 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} : 15 0^{\circ} + 18 0^{\circ} n

\frac{30 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

\frac{30 0 ^{\circ}}{2} = 15 0^{\circ}

\frac{30 0 ^{\circ}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{90 0 ^{\circ}}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= 15 0^{\circ}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Divide the numbers:

\frac{2}{2} = 1

= 18 0^{\circ} n

= 15 0^{\circ} + 18 0^{\circ} n

x = 15 0^{\circ} + 18 0^{\circ} n

x = 15 0^{\circ} + 18 0^{\circ} n

x = 15 0^{\circ} + 18 0^{\circ} n

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

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Frequently Asked Questions (FAQ)

What is the general solution for sin(30)=cos(2x) ?
The general solution for sin(30)=cos(2x) is x=30+180n,x=150+180n