What is the general solution for 10cos(B)+6=4cos(B)+4 ?

The general solution for 10cos(B)+6=4cos(B)+4 is B=1.91063…+2pin,B=-1.91063…+2pin

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Popular >

10cos(B)+6=4cos(B)+4

Solution

10 cos (B) + 6 = 4 cos (B) + 4

Solution

B = 1.91063 \dots + 2 πn, B = - 1.91063 \dots + 2 πn

Degrees

B = 109.47122 \dots^{\circ} + 36 0^{\circ} n, B = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

10 cos (B) + 6 = 4 cos (B) + 4

Solve by substitution

10 cos (B) + 6 = 4 cos (B) + 4

Let:

cos (B) = u

10 u + 6 = 4 u + 4

10 u + 6 = 4 u + 4 : u = - \frac{1}{3}

10 u + 6 = 4 u + 4

Move

6

to the right side

10 u + 6 = 4 u + 4

Subtract

6

from both sides

10 u + 6 - 6 = 4 u + 4 - 6

Simplify

10 u = 4 u - 2

10 u = 4 u - 2

Move

4 u

to the left side

10 u = 4 u - 2

Subtract

4 u

from both sides

10 u - 4 u = 4 u - 2 - 4 u

Simplify

6 u = - 2

6 u = - 2

Divide both sides by

6

6 u = - 2

Divide both sides by

6

\frac{6 u}{6} = \frac{- 2}{6}

Simplify

\frac{6 u}{6} = \frac{- 2}{6}

Simplify

\frac{6 u}{6} : u

\frac{6 u}{6}

Divide the numbers:

\frac{6}{6} = 1

= u

Simplify

\frac{- 2}{6} : - \frac{1}{3}

\frac{- 2}{6}

Apply the fraction rule:

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

= - \frac{2}{6}

Cancel the common factor:

2

= - \frac{1}{3}

u = - \frac{1}{3}

u = - \frac{1}{3}

u = - \frac{1}{3}

Substitute back

u = cos (B)

cos (B) = - \frac{1}{3}

cos (B) = - \frac{1}{3}

cos (B) = - \frac{1}{3} : B = arccos (- \frac{1}{3}) + 2 πn, B = - arccos (- \frac{1}{3}) + 2 πn

cos (B) = - \frac{1}{3}

Apply trig inverse properties

cos (B) = - \frac{1}{3}

General solutions for

cos (B) = - \frac{1}{3}

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

B = arccos (- \frac{1}{3}) + 2 πn, B = - arccos (- \frac{1}{3}) + 2 πn

B = arccos (- \frac{1}{3}) + 2 πn, B = - arccos (- \frac{1}{3}) + 2 πn

Combine all the solutions

B = arccos (- \frac{1}{3}) + 2 πn, B = - arccos (- \frac{1}{3}) + 2 πn

Show solutions in decimal form

B = 1.91063 \dots + 2 πn, B = - 1.91063 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 10cos(B)+6=4cos(B)+4 ?
The general solution for 10cos(B)+6=4cos(B)+4 is B=1.91063…+2pin,B=-1.91063…+2pin