What is the general solution for cos(3x)=sin(60) ?

The general solution for cos(3x)=sin(60) is x=10+(360n)/3 ,x=110+(360n)/3

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Popular >

cos(3x)=sin(60)

Solution

cos (3 x) = sin (6 0^{\circ})

Solution

x = 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}, x = 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

Radians

x = \frac{π}{18} + \frac{2 π}{3} n, x = \frac{11 π}{18} + \frac{2 π}{3} n

Solution steps

cos (3 x) = sin (6 0^{\circ})

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

= \frac{3}{2}

cos (3 x) = \frac{3}{2}

General solutions for

cos (3 x) = \frac{3}{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}

3 x = 3 0^{\circ} + 36 0^{\circ} n, 3 x = 33 0^{\circ} + 36 0^{\circ} n

3 x = 3 0^{\circ} + 36 0^{\circ} n, 3 x = 33 0^{\circ} + 36 0^{\circ} n

Solve

3 x = 3 0^{\circ} + 36 0^{\circ} n : x = 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

3 x = 3 0^{\circ} + 36 0^{\circ} n

Divide both sides by

3

3 x = 3 0^{\circ} + 36 0^{\circ} n

Divide both sides by

3

\frac{3 x}{3} = \frac{3 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

Simplify

\frac{3 x}{3} = \frac{3 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{3 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3} : 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

\frac{3 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

\frac{3 0 ^{\circ}}{3} = 1 0^{\circ}

\frac{3 0 ^{\circ}}{3}

Apply the fraction rule:

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

= \frac{18 0 ^{\circ}}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= 1 0^{\circ}

= 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

x = 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

x = 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

x = 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

Solve

3 x = 33 0^{\circ} + 36 0^{\circ} n : x = 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

3 x = 33 0^{\circ} + 36 0^{\circ} n

Divide both sides by

3

3 x = 33 0^{\circ} + 36 0^{\circ} n

Divide both sides by

3

\frac{3 x}{3} = \frac{33 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

Simplify

\frac{3 x}{3} = \frac{33 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{33 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3} : 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

\frac{33 0 ^{\circ}}{3} + \frac{36 0 ^{\circ} n}{3}

\frac{33 0 ^{\circ}}{3} = 11 0^{\circ}

\frac{33 0 ^{\circ}}{3}

Apply the fraction rule:

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

= \frac{198 0 ^{\circ}}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= 11 0^{\circ}

= 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

x = 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

x = 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

x = 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

x = 1 0^{\circ} + \frac{36 0 ^{\circ} n}{3}, x = 11 0^{\circ} + \frac{36 0 ^{\circ} n}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for cos(3x)=sin(60) ?
The general solution for cos(3x)=sin(60) is x=10+(360n)/3 ,x=110+(360n)/3