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Popular Trigonometry >

4cos(30x)+12=10.5

Solution

4 cos (30 x) + 12 = 10.5

Solution

x = \frac{1.95519 \dots}{30} + \frac{πn}{15}, x = - \frac{1.95519 \dots}{30} + \frac{πn}{15}

+1

Degrees

x = 3.73414 \dots^{\circ} + 1 2^{\circ} n, x = - 3.73414 \dots^{\circ} + 1 2^{\circ} n

Solution steps

4 cos (30 x) + 12 = 10.5

Move

12

to the right side

4 cos (30 x) + 12 = 10.5

Subtract

12

from both sides

4 cos (30 x) + 12 - 12 = 10.5 - 12

Simplify

4 cos (30 x) = - 1.5

4 cos (30 x) = - 1.5

Divide both sides by

4

4 cos (30 x) = - 1.5

Divide both sides by

4

\frac{4 cos ( 30 x )}{4} = \frac{- 1.5}{4}

Simplify

\frac{4 cos ( 30 x )}{4} = \frac{- 1.5}{4}

Simplify

\frac{4 cos ( 30 x )}{4} : cos (30 x)

\frac{4 cos ( 30 x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= cos (30 x)

Simplify

\frac{- 1.5}{4} : - 0.375

\frac{- 1.5}{4}

Apply the fraction rule:

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

= - \frac{1.5}{4}

Divide the numbers:

\frac{1.5}{4} = 0.375

= - 0.375

cos (30 x) = - 0.375

cos (30 x) = - 0.375

cos (30 x) = - 0.375

Apply trig inverse properties

cos (30 x) = - 0.375

General solutions for

cos (30 x) = - 0.375

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

30 x = arccos (- 0.375) + 2 πn, 30 x = - arccos (- 0.375) + 2 πn

30 x = arccos (- 0.375) + 2 πn, 30 x = - arccos (- 0.375) + 2 πn

Solve

30 x = arccos (- 0.375) + 2 πn : x = \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}

30 x = arccos (- 0.375) + 2 πn

Divide both sides by

30

30 x = arccos (- 0.375) + 2 πn

Divide both sides by

30

\frac{30 x}{30} = \frac{arccos ( - 0.375 )}{30} + \frac{2 πn}{30}

Simplify

x = \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}

x = \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}

Solve

30 x = - arccos (- 0.375) + 2 πn : x = - \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}

30 x = - arccos (- 0.375) + 2 πn

Divide both sides by

30

30 x = - arccos (- 0.375) + 2 πn

Divide both sides by

30

\frac{30 x}{30} = - \frac{arccos ( - 0.375 )}{30} + \frac{2 πn}{30}

Simplify

x = - \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}

x = - \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}

x = \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}, x = - \frac{arccos ( - 0.375 )}{30} + \frac{πn}{15}

Show solutions in decimal form

x = \frac{1.95519 \dots}{30} + \frac{πn}{15}, x = - \frac{1.95519 \dots}{30} + \frac{πn}{15}

Graph

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