What is the general solution for 8cos(B)+sqrt(52)=8 ?

The general solution for 8cos(B)+sqrt(52)=8 is B=1.47202…+2pin,B=2pi-1.47202…+2pin

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Popular >

8cos(B)+sqrt(52)=8

Solution

8 cos (B) + 52 = 8

Solution

B = 1.47202 \dots + 2 πn, B = 2 π - 1.47202 \dots + 2 πn

Degrees

B = 84.34074 \dots^{\circ} + 36 0^{\circ} n, B = 275.65925 \dots^{\circ} + 36 0^{\circ} n

Solution steps

8 cos (B) + 52 = 8

52 = 213

52

Prime factorization of

52 : 2^{2} \cdot 13

52

52

divides by

252 = 26 \cdot 2

= 2 \cdot 26

26

divides by

226 = 13 \cdot 2

= 2 \cdot 2 \cdot 13

2, 13

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 13

= 2^{2} \cdot 13

= 2^{2} \cdot 13

Apply radical rule:

= 13 2^{2}

Apply radical rule:

2^{2} = 2

= 213

8 cos (B) + 213 = 8

Move

213

to the right side

8 cos (B) + 213 = 8

Subtract

213

from both sides

8 cos (B) + 213 - 213 = 8 - 213

Simplify

8 cos (B) = 8 - 213

8 cos (B) = 8 - 213

Divide both sides by

8

8 cos (B) = 8 - 213

Divide both sides by

8

\frac{8 cos ( B )}{8} = \frac{8}{8} - \frac{2 13}{8}

Simplify

\frac{8 cos ( B )}{8} = \frac{8}{8} - \frac{2 13}{8}

Simplify

\frac{8 cos ( B )}{8} : cos (B)

\frac{8 cos ( B )}{8}

Divide the numbers:

\frac{8}{8} = 1

= cos (B)

Simplify

\frac{8}{8} - \frac{2 13}{8} : \frac{4 - 13}{4}

\frac{8}{8} - \frac{2 13}{8}

Apply rule

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

= \frac{8 - 2 13}{8}

Factor

8 - 213 : 2 (4 - 13)

8 - 213

Rewrite as

= 2 \cdot 4 - 213

Factor out common term

2

= 2 (4 - 13)

= \frac{2 ( 4 - 13 )}{8}

Cancel the common factor:

2

= \frac{4 - 13}{4}

cos (B) = \frac{4 - 13}{4}

cos (B) = \frac{4 - 13}{4}

cos (B) = \frac{4 - 13}{4}

Apply trig inverse properties

cos (B) = \frac{4 - 13}{4}

General solutions for

cos (B) = \frac{4 - 13}{4}

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

B = arccos (\frac{4 - 13}{4}) + 2 πn, B = 2 π - arccos (\frac{4 - 13}{4}) + 2 πn

B = arccos (\frac{4 - 13}{4}) + 2 πn, B = 2 π - arccos (\frac{4 - 13}{4}) + 2 πn

Show solutions in decimal form

B = 1.47202 \dots + 2 πn, B = 2 π - 1.47202 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 8cos(B)+sqrt(52)=8 ?
The general solution for 8cos(B)+sqrt(52)=8 is B=1.47202…+2pin,B=2pi-1.47202…+2pin