What is the general solution for cos(x)=(sqrt(8))/3 ?

The general solution for cos(x)=(sqrt(8))/3 is x=0.33983…+2pin,x=2pi-0.33983…+2pin

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cos(x)=(sqrt(8))/3

cos (x) = \frac{8}{3}

x = 0.33983 \dots + 2 πn, x = 2 π - 0.33983 \dots + 2 πn

Degrees

x = 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 340.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (x) = \frac{8}{3}

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

cos (x) = \frac{2 2}{3}

Apply trig inverse properties

cos (x) = \frac{2 2}{3}

General solutions for

cos (x) = \frac{2 2}{3}

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

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

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

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = 2 π - 0.33983 \dots + 2 πn

arctan (θ) = \frac{6}{8}

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

tan (θ) = \frac{- \frac{4}{3} - ( - \frac{11}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

8 + 2 cot (x) = 12

(1 + cot (p)) tan (p) = 3

What is the general solution for cos(x)=(sqrt(8))/3 ?
The general solution for cos(x)=(sqrt(8))/3 is x=0.33983…+2pin,x=2pi-0.33983…+2pin