What is the general solution for 3tan(c)+sqrt(8)=0 ?

The general solution for 3tan(c)+sqrt(8)=0 is c=-0.75596…+pin

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3tan(c)+sqrt(8)=0

3 tan (c) + 8 = 0

c = - 0.75596 \dots + πn

Degrees

c = - 43.31385 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 tan (c) + 8 = 0

Simplify

3 tan (c) + 8 : 3 tan (c) + 22

3 tan (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 tan (c) + 22

3 tan (c) + 22 = 0

Move

22

to the right side

3 tan (c) + 22 = 0

Subtract

22

from both sides

3 tan (c) + 22 - 22 = 0 - 22

Simplify

3 tan (c) = - 22

3 tan (c) = - 22

Divide both sides by

3

3 tan (c) = - 22

Divide both sides by

3

\frac{3 tan ( c )}{3} = \frac{- 2 2}{3}

Simplify

tan (c) = - \frac{2 2}{3}

tan (c) = - \frac{2 2}{3}

Apply trig inverse properties

tan (c) = - \frac{2 2}{3}

General solutions for

tan (c) = - \frac{2 2}{3}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

c = arctan (- \frac{2 2}{3}) + πn

c = arctan (- \frac{2 2}{3}) + πn

Show solutions in decimal form

c = - 0.75596 \dots + πn

What is the general solution for 3tan(c)+sqrt(8)=0 ?
The general solution for 3tan(c)+sqrt(8)=0 is c=-0.75596…+pin