What is the general solution for tan(B)=sqrt(8) ?

The general solution for tan(B)=sqrt(8) is B=1.23095…+pin

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tan(B)=sqrt(8)

tan (B) = 8

B = 1.23095 \dots + πn

Solution steps

tan (B) = 8

Simplify

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

Apply trig inverse properties

tan (B) = 22

General solutions for

tan (B) = 22

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

B = arctan (22) + πn

B = arctan (22) + πn

Show solutions in decimal form

B = 1.23095 \dots + πn

\frac{tan ( θ ) cot ( θ )}{sec ^{2} ( θ )} = cot (θ)

3 - 3 cot (x) = - 6 cot (x)

sin (y) = \frac{3}{2}

9 sin^{2} (x) + 3 cos (x) - 7 = 0

A, sin (B + \frac{C}{2}) = cos (\frac{A}{2})

What is the general solution for tan(B)=sqrt(8) ?
The general solution for tan(B)=sqrt(8) is B=1.23095…+pin