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Popular >

3/16 =1(cos(0))(cos(30))(cos(x-30))

Solution

\frac{3}{16} = 1 (cos (0)) (cos (3 0^{\circ})) (cos (x - 3 0^{\circ}))

Solution

x = 1.35256 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 36 0^{\circ} - 1.35256 \dots + 36 0^{\circ} n + 3 0^{\circ}

Radians

x = 1.35256 \dots + \frac{π}{6} + 2 πn, x = 2 π - 1.35256 \dots + \frac{π}{6} + 2 πn

Solution steps

\frac{3}{16} = 1 \cdot (cos (0)) (cos (3 0^{\circ})) (cos (x - 3 0^{\circ}))

Switch sides

1 \cdot cos (0) cos (3 0^{\circ}) cos (x - 3 0^{\circ}) = \frac{3}{16}

cos (0) = 1

cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

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}

= 1

= 1

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

cos (3 0^{\circ})

Use the following trivial identity:

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

cos (3 0^{\circ})

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}

= \frac{3}{2}

= \frac{3}{2}

1 \cdot 1 \cdot \frac{3}{2} cos (x - 3 0^{\circ}) = \frac{3}{16}

Simplify

1 \cdot 1 \cdot \frac{3}{2} : \frac{3}{2}

1 \cdot 1 \cdot \frac{3}{2}

Multiply:

1 \cdot 1 \cdot \frac{3}{2} = \frac{3}{2}

= \frac{3}{2}

\frac{3}{2} cos (x - 3 0^{\circ}) = \frac{3}{16}

Multiply both sides by

2

\frac{3}{2} cos (x - 3 0^{\circ}) = \frac{3}{16}

Multiply both sides by

2

2 \cdot \frac{3}{2} cos (x - 3 0^{\circ}) = \frac{3 \cdot 2}{16}

Simplify

2 \cdot \frac{3}{2} cos (x - 3 0^{\circ}) = \frac{3 \cdot 2}{16}

Simplify

2 \cdot \frac{3}{2} cos (x - 3 0^{\circ}) : 3 cos (x - 3 0^{\circ})

2 \cdot \frac{3}{2} cos (x - 3 0^{\circ})

Multiply fractions:

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

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

Cancel the common factor:

2

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

Simplify

\frac{3 \cdot 2}{16} : \frac{3}{8}

\frac{3 \cdot 2}{16}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6}{16}

Cancel the common factor:

2

= \frac{3}{8}

3 cos (x - 3 0^{\circ}) = \frac{3}{8}

3 cos (x - 3 0^{\circ}) = \frac{3}{8}

3 cos (x - 3 0^{\circ}) = \frac{3}{8}

Divide both sides by

3

3 cos (x - 3 0^{\circ}) = \frac{3}{8}

Divide both sides by

3

\frac{3 cos ( x - 3 0 ^{\circ} )}{3} = \frac{\frac{3}{8}}{3}

Simplify

\frac{3 cos ( x - 3 0 ^{\circ} )}{3} = \frac{\frac{3}{8}}{3}

Simplify

\frac{3 cos ( x - 3 0 ^{\circ} )}{3} : cos (x - 3 0^{\circ})

\frac{3 cos ( x - 3 0 ^{\circ} )}{3}

Cancel the common factor:

3

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

Simplify

\frac{\frac{3}{8}}{3} : \frac{3}{8}

\frac{\frac{3}{8}}{3}

Apply the fraction rule:

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

= \frac{3}{8 3}

Apply radical rule:

n a = a^{\frac{1}{n}}

3 = 3^{\frac{1}{2}}

= \frac{3}{8 \cdot 3 ^{\frac{1}{2}}}

Apply exponent rule:

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

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= \frac{3 ^{1 - \frac{1}{2}}}{8}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{3 ^{\frac{1}{2}}}{8}

Apply radical rule:

a^{\frac{1}{n}} = n a

3^{\frac{1}{2}} = 3

= \frac{3}{8}

cos (x - 3 0^{\circ}) = \frac{3}{8}

cos (x - 3 0^{\circ}) = \frac{3}{8}

cos (x - 3 0^{\circ}) = \frac{3}{8}

Apply trig inverse properties

cos (x - 3 0^{\circ}) = \frac{3}{8}

General solutions for

cos (x - 3 0^{\circ}) = \frac{3}{8}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

x - 3 0^{\circ} = arccos (\frac{3}{8}) + 36 0^{\circ} n, x - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n

x - 3 0^{\circ} = arccos (\frac{3}{8}) + 36 0^{\circ} n, x - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n

Solve

x - 3 0^{\circ} = arccos (\frac{3}{8}) + 36 0^{\circ} n : x = arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = arccos (\frac{3}{8}) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = arccos (\frac{3}{8}) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

x = arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

Solve

x - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

x = arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{3}{8}) + 36 0^{\circ} n + 3 0^{\circ}

Show solutions in decimal form

x = 1.35256 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 36 0^{\circ} - 1.35256 \dots + 36 0^{\circ} n + 3 0^{\circ}

Graph

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