What is the general solution for 3cos(C)+sqrt(8)=0 ?

The general solution for 3cos(C)+sqrt(8)=0 is C=2.80175…+2pin,C=-2.80175…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

3cos(C)+sqrt(8)=0

3 cos (C) + 8 = 0

C = 2.80175 \dots + 2 πn, C = - 2.80175 \dots + 2 πn

Degrees

C = 160.52877 \dots^{\circ} + 36 0^{\circ} n, C = - 160.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (C) + 8 = 0

Simplify

3 cos (C) + 8 : 3 cos (C) + 22

3 cos (C) + 8

8 = 22

8

Prime factorization of

8 : 2^{3}

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

2

is a prime number, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2

= 2^{3}

= 2^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= 2^{2} \cdot 2

Apply radical rule:

= 2 2^{2}

Apply radical rule:

2^{2} = 2

= 22

= 3 cos (C) + 22

3 cos (C) + 22 = 0

Move

22

to the right side

3 cos (C) + 22 = 0

Subtract

22

from both sides

3 cos (C) + 22 - 22 = 0 - 22

Simplify

3 cos (C) = - 22

3 cos (C) = - 22

Divide both sides by

3

3 cos (C) = - 22

Divide both sides by

3

\frac{3 cos ( C )}{3} = \frac{- 2 2}{3}

Simplify

cos (C) = - \frac{2 2}{3}

cos (C) = - \frac{2 2}{3}

Apply trig inverse properties

cos (C) = - \frac{2 2}{3}

General solutions for

cos (C) = - \frac{2 2}{3}

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

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

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

Show solutions in decimal form

C = 2.80175 \dots + 2 πn, C = - 2.80175 \dots + 2 πn

What is the general solution for 3cos(C)+sqrt(8)=0 ?
The general solution for 3cos(C)+sqrt(8)=0 is C=2.80175…+2pin,C=-2.80175…+2pin