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Popular Trigonometry >

16cos(15x)+8=2

Solution

16 cos (15 x) + 8 = 2

Solution

x = \frac{1.95519 \dots}{15} + \frac{2 πn}{15}, x = - \frac{1.95519 \dots}{15} + \frac{2 πn}{15}

+1

Degrees

x = 7.46828 \dots^{\circ} + 2 4^{\circ} n, x = - 7.46828 \dots^{\circ} + 2 4^{\circ} n

Solution steps

16 cos (15 x) + 8 = 2

Move

8

to the right side

16 cos (15 x) + 8 = 2

Subtract

8

from both sides

16 cos (15 x) + 8 - 8 = 2 - 8

Simplify

16 cos (15 x) = - 6

16 cos (15 x) = - 6

Divide both sides by

16

16 cos (15 x) = - 6

Divide both sides by

16

\frac{16 cos ( 15 x )}{16} = \frac{- 6}{16}

Simplify

\frac{16 cos ( 15 x )}{16} = \frac{- 6}{16}

Simplify

\frac{16 cos ( 15 x )}{16} : cos (15 x)

\frac{16 cos ( 15 x )}{16}

Divide the numbers:

\frac{16}{16} = 1

= cos (15 x)

Simplify

\frac{- 6}{16} : - \frac{3}{8}

\frac{- 6}{16}

Apply the fraction rule:

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

= - \frac{6}{16}

Cancel the common factor:

2

= - \frac{3}{8}

cos (15 x) = - \frac{3}{8}

cos (15 x) = - \frac{3}{8}

cos (15 x) = - \frac{3}{8}

Apply trig inverse properties

cos (15 x) = - \frac{3}{8}

General solutions for

cos (15 x) = - \frac{3}{8}

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

15 x = arccos (- \frac{3}{8}) + 2 πn, 15 x = - arccos (- \frac{3}{8}) + 2 πn

15 x = arccos (- \frac{3}{8}) + 2 πn, 15 x = - arccos (- \frac{3}{8}) + 2 πn

Solve

15 x = arccos (- \frac{3}{8}) + 2 πn : x = \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

15 x = arccos (- \frac{3}{8}) + 2 πn

Divide both sides by

15

15 x = arccos (- \frac{3}{8}) + 2 πn

Divide both sides by

15

\frac{15 x}{15} = \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

Simplify

x = \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

x = \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

Solve

15 x = - arccos (- \frac{3}{8}) + 2 πn : x = - \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

15 x = - arccos (- \frac{3}{8}) + 2 πn

Divide both sides by

15

15 x = - arccos (- \frac{3}{8}) + 2 πn

Divide both sides by

15

\frac{15 x}{15} = - \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

Simplify

x = - \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

x = - \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

x = \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}, x = - \frac{arccos ( - \frac{3}{8} )}{15} + \frac{2 πn}{15}

Show solutions in decimal form

x = \frac{1.95519 \dots}{15} + \frac{2 πn}{15}, x = - \frac{1.95519 \dots}{15} + \frac{2 πn}{15}

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